अभाज्य गुणनखंडन में \(18^2\times5\) को अंतिम रूप क्यों नहीं माना जाता?
Why is \(18^2\times5\) not considered the final form in prime factorisation?
#prime-factorisation
#composite-base
#hard
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A क्योंकि 18 संयुक्त संख्या है / Because 18 is composite
B क्योंकि 5 संयुक्त संख्या है / Because 5 is composite
C क्योंकि घात का प्रयोग नहीं किया जा सकता / Because powers cannot be used
D क्योंकि गुणनफल बदल जाता है / Because the product changes
Explanation opens after your attempt
Correct Answer
A. क्योंकि 18 संयुक्त संख्या है / Because 18 is composite
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में आधार अभाज्य होने चाहिए। / In the final prime factorisation, bases must be prime.
Step 2
Why this answer is correct
\(18=2\times3^2\), इसलिए \(18^2\) को \(2^2\times3^4\) में बदलना होगा। / \(18=2\times3^2\), so \(18^2\) must be changed into \(2^2\times3^4\).
Step 3
Exam Tip
संयुक्त आधार को अंतिम उत्तर में न छोड़ें। / Do not leave a composite base in the final answer.
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संख्या 2376 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2376?
#prime-factorisation
#number-2376
#hard
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A \(2^3\times3^3\times11\)
B \(2^2\times3^3\times11\)
C \(8\times297\)
D \(2^3\times27\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times11\)
Step 1
Concept
\(2376=8\times297\) लिखें। / Write \(2376=8\times297\).
Step 2
Why this answer is correct
\(8=2^3\) और \(297=3^3\times11\), इसलिए \(2376=2^3\times3^3\times11\)। / \(8=2^3\) and \(297=3^3\times11\), so \(2376=2^3\times3^3\times11\).
Step 3
Exam Tip
297 को अंतिम रूप में न छोड़ें। / Do not leave 297 in the final form.
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संख्या 3465 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 3465?
#prime-factorisation
#number-3465
#hard
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A \(3^2\times5\times7\times11\)
B \(3\times5\times7\times11\)
C \(9\times385\)
D \(45\times77\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5\times7\times11\)
Step 1
Concept
\(3465=9\times385\) लिखें। / Write \(3465=9\times385\).
Step 2
Why this answer is correct
\(9=3^2\) और \(385=5\times7\times11\), इसलिए \(3465=3^2\times5\times7\times11\)। / \(9=3^2\) and \(385=5\times7\times11\), so \(3465=3^2\times5\times7\times11\).
Step 3
Exam Tip
385 को भी पूरा अभाज्य रूप दें। / Give 385 its complete prime form too.
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संख्या 4410 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 4410?
#prime-factorisation
#number-4410
#hard
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A \(2\times3^2\times5\times7^2\)
B \(2^2\times3\times5\times7^2\)
C \(90\times49\)
D \(2\times45\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\times7^2\)
Step 1
Concept
\(4410=90\times49\) लिखें। / Write \(4410=90\times49\).
Step 2
Why this answer is correct
\(90=2\times3^2\times5\) और \(49=7^2\), इसलिए \(4410=2\times3^2\times5\times7^2\)। / \(90=2\times3^2\times5\) and \(49=7^2\), so \(4410=2\times3^2\times5\times7^2\).
Step 3
Exam Tip
90 और 49 दोनों को अभाज्य रूप दें। / Give prime form to both 90 and 49.
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संख्या 5040 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 5040?
#prime-factorisation
#number-5040
#hard
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A \(2^4\times3^2\times5\times7\)
B \(2^3\times3^2\times5\times7\)
C \(16\times315\)
D \(2^4\times9\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^2\times5\times7\)
Step 1
Concept
\(5040=16\times315\) लिखें। / Write \(5040=16\times315\).
Step 2
Why this answer is correct
\(16=2^4\) और \(315=3^2\times5\times7\), इसलिए \(5040=2^4\times3^2\times5\times7\)। / \(16=2^4\) and \(315=3^2\times5\times7\), so \(5040=2^4\times3^2\times5\times7\).
Step 3
Exam Tip
315 को पूरा अभाज्य रूप दें। / Give 315 its complete prime form.
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संख्या 5292 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 5292?
#prime-factorisation
#number-5292
#hard
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A \(2^2\times3^3\times7^2\)
B \(2^3\times3^2\times7^2\)
C \(4\times1323\)
D \(12\times441\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\times7^2\)
Step 1
Concept
\(5292=4\times1323\) लिखें। / Write \(5292=4\times1323\).
Step 2
Why this answer is correct
\(4=2^2\) और \(1323=3^3\times7^2\), इसलिए \(5292=2^2\times3^3\times7^2\)। / \(4=2^2\) and \(1323=3^3\times7^2\), so \(5292=2^2\times3^3\times7^2\).
Step 3
Exam Tip
1323 को 3 और 7 की घातों में बदलें। / Convert 1323 into powers of 3 and 7.
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संख्या 5670 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 5670?
#prime-factorisation
#number-5670
#hard
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A \(2\times3^4\times5\times7\)
B \(2\times3^3\times5\times7\)
C \(81\times70\)
D \(2\times81\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^4\times5\times7\)
Step 1
Concept
\(5670=81\times70\) लिखें। / Write \(5670=81\times70\).
Step 2
Why this answer is correct
\(81=3^4\) और \(70=2\times5\times7\), इसलिए \(5670=2\times3^4\times5\times7\)। / \(81=3^4\) and \(70=2\times5\times7\), so \(5670=2\times3^4\times5\times7\).
Step 3
Exam Tip
81 को \(3^4\) में बदलना जरूरी है। / It is necessary to change 81 into \(3^4\).
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संख्या 7350 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 7350?
#prime-factorisation
#number-7350
#hard
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A \(2\times3\times5^2\times7^2\)
B \(2^2\times3\times5\times7^2\)
C \(150\times49\)
D \(2\times75\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5^2\times7^2\)
Step 1
Concept
\(7350=150\times49\) लिखें। / Write \(7350=150\times49\).
Step 2
Why this answer is correct
\(150=2\times3\times5^2\) और \(49=7^2\), इसलिए \(7350=2\times3\times5^2\times7^2\)। / \(150=2\times3\times5^2\) and \(49=7^2\), so \(7350=2\times3\times5^2\times7^2\).
Step 3
Exam Tip
150 और 49 को अलग-अलग पूरा तोड़ें। / Break 150 and 49 completely and separately.
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संख्या 7560 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 7560?
#prime-factorisation
#number-7560
#hard
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A \(2^3\times3^3\times5\times7\)
B \(2^2\times3^3\times5\times7\)
C \(8\times945\)
D \(2^3\times27\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times5\times7\)
Step 1
Concept
\(7560=8\times945\) लिखें। / Write \(7560=8\times945\).
Step 2
Why this answer is correct
\(8=2^3\) और \(945=3^3\times5\times7\), इसलिए \(7560=2^3\times3^3\times5\times7\)। / \(8=2^3\) and \(945=3^3\times5\times7\), so \(7560=2^3\times3^3\times5\times7\).
Step 3
Exam Tip
945 को अंतिम रूप में न छोड़ें। / Do not leave 945 in the final form.
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संख्या 8085 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 8085?
#prime-factorisation
#number-8085
#hard
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A \(3\times5\times7^2\times11\)
B \(3^2\times5\times7\times11\)
C \(15\times539\)
D \(3\times2695\)
Explanation opens after your attempt
Correct Answer
A. \(3\times5\times7^2\times11\)
Step 1
Concept
\(8085=15\times539\) लिखें। / Write \(8085=15\times539\).
Step 2
Why this answer is correct
\(15=3\times5\) और \(539=7^2\times11\), इसलिए \(8085=3\times5\times7^2\times11\)। / \(15=3\times5\) and \(539=7^2\times11\), so \(8085=3\times5\times7^2\times11\).
Step 3
Exam Tip
539 को भी पूरा अभाज्य रूप दें। / Give 539 its complete prime form too.
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संख्या 8820 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 8820?
#prime-factorisation
#number-8820
#hard
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A \(2^2\times3^2\times5\times7^2\)
B \(2\times3^2\times5\times7^2\)
C \(180\times49\)
D \(4\times2205\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times5\times7^2\)
Step 1
Concept
\(8820=180\times49\) लिखें। / Write \(8820=180\times49\).
Step 2
Why this answer is correct
\(180=2^2\times3^2\times5\) और \(49=7^2\), इसलिए \(8820=2^2\times3^2\times5\times7^2\)। / \(180=2^2\times3^2\times5\) and \(49=7^2\), so \(8820=2^2\times3^2\times5\times7^2\).
Step 3
Exam Tip
180 और 49 को अभाज्य घातों में बदलें। / Convert 180 and 49 into prime powers.
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संख्या 9800 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 9800?
#prime-factorisation
#number-9800
#hard
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A \(2^3\times5^2\times7^2\)
B \(2^2\times5^2\times7^2\)
C \(8\times1225\)
D \(2^3\times35^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times5^2\times7^2\)
Step 1
Concept
\(9800=8\times1225\) लिखें। / Write \(9800=8\times1225\).
Step 2
Why this answer is correct
\(8=2^3\) और \(1225=5^2\times7^2\), इसलिए \(9800=2^3\times5^2\times7^2\)। / \(8=2^3\) and \(1225=5^2\times7^2\), so \(9800=2^3\times5^2\times7^2\).
Step 3
Exam Tip
1225 को अंतिम रूप में न छोड़ें। / Do not leave 1225 in the final form.
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संख्या 10368 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 10368?
#prime-factorisation
#number-10368
#hard
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A \(2^7\times3^4\)
B \(2^6\times3^4\)
C \(128\times81\)
D \(2^7\times27\times3\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^4\)
Step 1
Concept
\(10368=128\times81\) लिखें। / Write \(10368=128\times81\).
Step 2
Why this answer is correct
\(128=2^7\) और \(81=3^4\), इसलिए \(10368=2^7\times3^4\)। / \(128=2^7\) and \(81=3^4\), so \(10368=2^7\times3^4\).
Step 3
Exam Tip
128 और 81 दोनों को अभाज्य घातों में लिखें। / Write both 128 and 81 as prime powers.
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संख्या 12320 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 12320?
#prime-factorisation
#number-12320
#hard
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A \(2^5\times5\times7\times11\)
B \(2^4\times5\times7\times11\)
C \(32\times385\)
D \(2^5\times35\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times5\times7\times11\)
Step 1
Concept
\(12320=32\times385\) लिखें। / Write \(12320=32\times385\).
Step 2
Why this answer is correct
\(32=2^5\) और \(385=5\times7\times11\), इसलिए \(12320=2^5\times5\times7\times11\)। / \(32=2^5\) and \(385=5\times7\times11\), so \(12320=2^5\times5\times7\times11\).
Step 3
Exam Tip
385 को पूरा अभाज्य रूप दें। / Give 385 its complete prime form.
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संख्या 13230 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 13230?
#prime-factorisation
#number-13230
#hard
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A \(2\times3^3\times5\times7^2\)
B \(2^2\times3^2\times5\times7^2\)
C \(270\times49\)
D \(2\times135\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^3\times5\times7^2\)
Step 1
Concept
\(13230=270\times49\) लिखें। / Write \(13230=270\times49\).
Step 2
Why this answer is correct
\(270=2\times3^3\times5\) और \(49=7^2\), इसलिए \(13230=2\times3^3\times5\times7^2\)। / \(270=2\times3^3\times5\) and \(49=7^2\), so \(13230=2\times3^3\times5\times7^2\).
Step 3
Exam Tip
270 और 49 को अंतिम रूप में न रखें। / Do not keep 270 and 49 in the final form.
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संख्या 14700 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 14700?
#prime-factorisation
#number-14700
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^2\times3\times5^2\times7^2\)
B \(2\times3^2\times5^2\times7^2\)
C \(300\times49\)
D \(4\times3675\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times5^2\times7^2\)
Step 1
Concept
\(14700=300\times49\) लिखें। / Write \(14700=300\times49\).
Step 2
Why this answer is correct
\(300=2^2\times3\times5^2\) और \(49=7^2\), इसलिए \(14700=2^2\times3\times5^2\times7^2\)। / \(300=2^2\times3\times5^2\) and \(49=7^2\), so \(14700=2^2\times3\times5^2\times7^2\).
Step 3
Exam Tip
300 को अभाज्य घातों में बदलें। / Convert 300 into prime powers.
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संख्या 15840 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 15840?
#prime-factorisation
#number-15840
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^5\times3^2\times5\times11\)
B \(2^4\times3^2\times5\times11\)
C \(32\times495\)
D \(2^5\times45\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^2\times5\times11\)
Step 1
Concept
\(15840=32\times495\) लिखें। / Write \(15840=32\times495\).
Step 2
Why this answer is correct
\(32=2^5\) और \(495=3^2\times5\times11\), इसलिए \(15840=2^5\times3^2\times5\times11\)। / \(32=2^5\) and \(495=3^2\times5\times11\), so \(15840=2^5\times3^2\times5\times11\).
Step 3
Exam Tip
495 को पूरा अभाज्य रूप दें। / Give 495 its complete prime form.
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संख्या 17640 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 17640?
#prime-factorisation
#number-17640
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^3\times3^2\times5\times7^2\)
B \(2^4\times3^2\times5\times7\)
C \(8\times2205\)
D \(2^3\times45\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times7^2\)
Step 1
Concept
\(17640=8\times2205\) लिखें। / Write \(17640=8\times2205\).
Step 2
Why this answer is correct
\(2205=3^2\times5\times7^2\), इसलिए \(17640=2^3\times3^2\times5\times7^2\)। / \(2205=3^2\times5\times7^2\), so \(17640=2^3\times3^2\times5\times7^2\).
Step 3
Exam Tip
2205 को पूरा अभाज्य रूप दें। / Give 2205 its complete prime form.
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संख्या 20736 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 20736?
#prime-factorisation
#square-number
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^8\times3^4\)
B \(2^7\times3^4\)
C \(256\times81\)
D \(144^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^8\times3^4\)
Step 1
Concept
\(20736=256\times81\) लिखें। / Write \(20736=256\times81\).
Step 2
Why this answer is correct
\(256=2^8\) और \(81=3^4\), इसलिए \(20736=2^8\times3^4\)। / \(256=2^8\) and \(81=3^4\), so \(20736=2^8\times3^4\).
Step 3
Exam Tip
256 और 81 को अभाज्य घातों में बदलें। / Convert 256 and 81 into prime powers.
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संख्या 22050 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 22050?
#prime-factorisation
#number-22050
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2\times3^2\times5^2\times7^2\)
B \(2^2\times3\times5^2\times7^2\)
C \(450\times49\)
D \(2\times225\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5^2\times7^2\)
Step 1
Concept
\(22050=450\times49\) लिखें। / Write \(22050=450\times49\).
Step 2
Why this answer is correct
\(450=2\times3^2\times5^2\) और \(49=7^2\), इसलिए \(22050=2\times3^2\times5^2\times7^2\)। / \(450=2\times3^2\times5^2\) and \(49=7^2\), so \(22050=2\times3^2\times5^2\times7^2\).
Step 3
Exam Tip
450 को पूरा अभाज्य रूप दें। / Give 450 its complete prime form.
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संख्या 27720 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 27720?
#prime-factorisation
#number-27720
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^3\times3^2\times5\times7\times11\)
B \(2^2\times3^3\times5\times7\times11\)
C \(8\times3465\)
D \(2^3\times9\times385\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times7\times11\)
Step 1
Concept
\(27720=8\times3465\) लिखें। / Write \(27720=8\times3465\).
Step 2
Why this answer is correct
\(3465=3^2\times5\times7\times11\), इसलिए \(27720=2^3\times3^2\times5\times7\times11\)। / \(3465=3^2\times5\times7\times11\), so \(27720=2^3\times3^2\times5\times7\times11\).
Step 3
Exam Tip
3465 को पूरा अभाज्य रूप दें। / Give 3465 its complete prime form.
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यदि \(15840=2^a\times3^2\times5\times11\), तो (a) का मान क्या है?
If \(15840=2^a\times3^2\times5\times11\), what is the value of (a)?
#exponent-comparison
#number-15840
#hard
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? Hint Small clue
A 5
B 4
C 6
D 3
Explanation opens after your attempt
Step 1
Concept
\(15840=32\times495\) है। / \(15840=32\times495\).
Step 2
Why this answer is correct
\(32=2^5\) और \(495=3^2\times5\times11\), इसलिए 2 की घात 5 है। / \(32=2^5\) and \(495=3^2\times5\times11\), so the power of 2 is 5.
Step 3
Exam Tip
तुलना करने पर (a=5) मिलेगा। / Comparing gives (a=5).
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यदि \(22050=2\times3^b\times5^2\times7^2\), तो (b) का मान क्या है?
If \(22050=2\times3^b\times5^2\times7^2\), what is the value of (b)?
#exponent-comparison
#number-22050
#hard
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? Hint Small clue
A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
\(22050=450\times49\) लिखें। / Write \(22050=450\times49\).
Step 2
Why this answer is correct
\(450=2\times3^2\times5^2\) और \(49=7^2\), इसलिए 3 की घात 2 है। / \(450=2\times3^2\times5^2\) and \(49=7^2\), so the power of 3 is 2.
Step 3
Exam Tip
दिए गए रूप से तुलना करने पर (b=2) है। / Comparing with the given form gives (b=2).
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यदि \(20736=2^m\times3^4\), तो (m) का मान क्या है?
If \(20736=2^m\times3^4\), what is the value of (m)?
#exponent-comparison
#number-20736
#hard
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? Hint Small clue
A 8
B 7
C 6
D 9
Explanation opens after your attempt
Step 1
Concept
\(20736=256\times81\) लिखा जा सकता है। / (20736) can be written as \(256\times81\).
Step 2
Why this answer is correct
\(256=2^8\) और \(81=3^4\), इसलिए \(20736=2^8\times3^4\)। / \(256=2^8\) and \(81=3^4\), so \(20736=2^8\times3^4\).
Step 3
Exam Tip
तुलना करने पर (m=8) है। / Comparing gives (m=8).
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यदि \(27720=2^3\times3^2\times5\times7\times11\), तो इसमें अलग-अलग अभाज्य गुणनखंड कितने हैं?
If \(27720=2^3\times3^2\times5\times7\times11\), how many distinct prime factors does it have?
#distinct-prime-factors
#prime-exponents
#hard
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? Hint Small clue
A 5
B 8
C 6
D 11
Explanation opens after your attempt
Step 1
Concept
अलग-अलग अभाज्य गुणनखंडों में घातों को नहीं जोड़ा जाता। / For distinct prime factors, exponents are not added.
Step 2
Why this answer is correct
आधार 2, 3, 5, 7 और 11 हैं। / The bases are 2, 3, 5, 7, and 11.
Step 3
Exam Tip
इसलिए अलग-अलग अभाज्य गुणनखंड 5 हैं। / Therefore, there are 5 distinct prime factors.
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times3^3\times11\) है?
Which number has prime factorisation \(2^3\times3^3\times11\)?
#evaluate-factorisation
#number-2376
#hard
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A 2376
B 1188
C 4752
D 3564
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) और \(3^3=27\) निकालें। / Calculate \(2^3=8\) and \(3^3=27\).
Step 2
Why this answer is correct
\(8\times27\times11=2376\)। / \(8\times27\times11=2376\).
Step 3
Exam Tip
घातों का मान पहले निकालना सही तरीका है। / Finding powers first is the correct method.
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किस संख्या का अभाज्य गुणनखंडन \(3^2\times5\times7\times11\) है?
Which number has prime factorisation \(3^2\times5\times7\times11\)?
#evaluate-factorisation
#number-3465
#hard
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A 3465
B 1732
C 6930
D 1155
Explanation opens after your attempt
Step 1
Concept
\(3^2=9\) निकालें। / Calculate \(3^2=9\).
Step 2
Why this answer is correct
\(9\times5\times7\times11=3465\)। / \(9\times5\times7\times11=3465\).
Step 3
Exam Tip
कई गुणनखंड हों तो जोड़े बनाकर गुणा करें। / When there are many factors, multiply in pairs.
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किस संख्या का अभाज्य गुणनखंडन \(2^4\times3^2\times5\times7\) है?
Which number has prime factorisation \(2^4\times3^2\times5\times7\)?
#evaluate-factorisation
#number-5040
#hard
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? Hint Small clue
A 5040
B 2520
C 10080
D 7560
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(3^2=9\) निकालें। / Calculate \(2^4=16\) and \(3^2=9\).
Step 2
Why this answer is correct
\(16\times9\times5\times7=5040\)। / \(16\times9\times5\times7=5040\).
Step 3
Exam Tip
पहले \(16\times9=144\) करें, फिर बाकी गुणा करें। / First do \(16\times9=144\), then multiply the rest.
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किस संख्या का अभाज्य गुणनखंडन \(2^2\times3^3\times7^2\) है?
Which number has prime factorisation \(2^2\times3^3\times7^2\)?
#evaluate-factorisation
#number-5292
#hard
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A 5292
B 2646
C 10584
D 4410
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\), \(3^3=27\) और \(7^2=49\) निकालें। / Calculate \(2^2=4\), \(3^3=27\), and \(7^2=49\).
Step 2
Why this answer is correct
\(4\times27\times49=5292\)। / \(4\times27\times49=5292\).
Step 3
Exam Tip
तीनों घातों को अलग-अलग सरल करें। / Simplify all three powers separately.
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किस संख्या का अभाज्य गुणनखंडन \(2^7\times3^4\) है?
Which number has prime factorisation \(2^7\times3^4\)?
#evaluate-factorisation
#number-10368
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A 10368
B 5184
C 20736
D 7776
Explanation opens after your attempt
Step 1
Concept
\(2^7=128\) और \(3^4=81\) निकालें। / Calculate \(2^7=128\) and \(3^4=81\).
Step 2
Why this answer is correct
\(128\times81=10368\)। / \(128\times81=10368\).
Step 3
Exam Tip
बड़ी घातों को पहले हल करने से गलती कम होती है। / Solving large powers first reduces mistakes.
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यदि संख्या \(2^7\times3^2\times5^3\times11\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^7\times3^2\times5^3\times11\), by which smallest number should it be multiplied to make a perfect square?
#perfect-square
#prime-exponents
#hard
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? Hint Small clue
A 110
B 10
C 55
D 22
Explanation opens after your attempt
Step 1
Concept
पूर्ण वर्ग में सभी घातें सम होती हैं। / In a perfect square, all exponents are even.
Step 2
Why this answer is correct
2 की घात 7, 5 की घात 3 और 11 की घात 1 विषम हैं। / Powers of 2, 5, and 11 are odd.
Step 3
Exam Tip
\(2\times5\times11=110\) से गुणा करने पर सभी घातें सम हो जाएंगी। / Multiplying by \(2\times5\times11=110\) makes all exponents even.
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यदि संख्या \(2^6\times3^5\times7^2\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^6\times3^5\times7^2\), by which smallest number should it be divided to make a perfect square?
#perfect-square
#division
#hard
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? Hint Small clue
A 3
B 9
C 21
D 7
Explanation opens after your attempt
Step 1
Concept
पूर्ण वर्ग में सभी घातें सम होनी चाहिए। / In a perfect square, all exponents should be even.
Step 2
Why this answer is correct
केवल 3 की घात 5 विषम है। / Only the power of 3 is odd.
Step 3
Exam Tip
3 से भाग देने पर 3 की घात 4 हो जाएगी और संख्या पूर्ण वर्ग बनेगी। / Dividing by 3 makes the power of 3 equal to 4 and the number becomes a perfect square.
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यदि संख्या \(2^5\times3^4\times5^2\times7\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^5\times3^4\times5^2\times7\), by which smallest number should it be multiplied to make a perfect cube?
#perfect-cube
#prime-exponents
#hard
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? Hint Small clue
A \(2\times3^2\times5\times7^2\)
B \(2\times3\times5\times7\)
C \(3^2\times7^2\)
D \(2^2\times5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\times7^2\)
Step 1
Concept
पूर्ण घन में घातें 3 के गुणज होती हैं। / In a perfect cube, exponents are multiples of 3.
Step 2
Why this answer is correct
2 की घात 5 को 6, 3 की घात 4 को 6, 5 की घात 2 को 3 और 7 की घात 1 को 3 बनाना होगा। / Powers 5, 4, 2, and 1 must become 6, 6, 3, and 3.
Step 3
Exam Tip
सबसे छोटा गुणक \(2\times3^2\times5\times7^2\) है। / The smallest multiplier is \(2\times3^2\times5\times7^2\).
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यदि संख्या \(2^8\times3^7\times5^4\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^8\times3^7\times5^4\), by which smallest number should it be divided to make a perfect cube?
#perfect-cube
#division
#hard
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? Hint Small clue
A \(2^2\times3\times5\)
B \(2\times3\times5\)
C \(2^2\times3^2\times5\)
D \(2\times5\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times5\)
Step 1
Concept
पूर्ण घन के लिए घातें 3 के गुणज चाहिए। / For a perfect cube, exponents should be multiples of 3.
Step 2
Why this answer is correct
8 को 6, 7 को 6 और 4 को 3 तक घटाना सबसे छोटा तरीका है। / Reducing 8 to 6, 7 to 6, and 4 to 3 is the smallest way.
Step 3
Exam Tip
इसलिए भाजक \(2^2\times3\times5\) होगा। / Therefore, the divisor is \(2^2\times3\times5\).
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यदि \(n=2^5\times3^4\times5^2\times7\), तो (n) किस संख्या से विभाज्य नहीं होगा?
If \(n=2^5\times3^4\times5^2\times7\), by which number will (n) not be divisible?
#divisibility
#prime-exponents
#hard
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A \(2^6\)
B \(2^4\times3^2\)
C \(3^4\times5\)
D \(2^5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\)
Step 1
Concept
किसी भाजक की हर अभाज्य घात संख्या में उपलब्ध होनी चाहिए। / Every prime power of a divisor must be available in the number.
Step 2
Why this answer is correct
(n) में 2 की घात 5 है, लेकिन \(2^6\) के लिए 6 चाहिए। / (n) has power 5 of 2, but \(2^6\) needs 6.
Step 3
Exam Tip
इसलिए (n), \(2^6\) से विभाज्य नहीं होगा। / Therefore, (n) is not divisible by \(2^6\).
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यदि \(n=2^6\times3^2\times5^5\times11\), तो (n) किस संख्या से अवश्य विभाज्य होगा?
If \(n=2^6\times3^2\times5^5\times11\), by which number must (n) be divisible?
#divisibility
#prime-exponents
#hard
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? Hint Small clue
A \(2^5\times3\times5^4\times11\)
B \(2^7\times3\times5^4\)
C \(3^3\times5^2\)
D \(2^6\times5^6\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3\times5^4\times11\)
Step 1
Concept
विभाज्यता के लिए भाजक की घातें संख्या की घातों से अधिक नहीं होनी चाहिए। / For divisibility, exponents in the divisor must not exceed those in the number.
Step 2
Why this answer is correct
\(2^5\), (3), \(5^4\) और 11 सभी (n) में उपलब्ध हैं। / \(2^5\), (3), \(5^4\), and 11 are all available in (n).
Step 3
Exam Tip
इसलिए (n) इस संख्या से अवश्य विभाज्य होगा। / Therefore, (n) must be divisible by this number.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^6\times3^4\times5^3\times7^2\) है, तो दोहराव सहित अभाज्य गुणनखंडों की संख्या कितनी है?
If a number has prime factorisation \(2^6\times3^4\times5^3\times7^2\), how many prime factors does it have with repetition?
#counting-prime-factors
#prime-exponents
#hard
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? Hint Small clue
A 15
B 4
C 12
D 10
Explanation opens after your attempt
Step 1
Concept
दोहराव सहित गिनती में घातों को जोड़ा जाता है। / For counting with repetition, add the exponents.
Step 2
Why this answer is correct
(6+4+3+2=15)। / (6+4+3+2=15).
Step 3
Exam Tip
अलग-अलग आधारों की संख्या और दोहराव सहित संख्या में अंतर याद रखें। / Remember the difference between the number of distinct bases and the count with repetition.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4\times3^7\times11^3\times13^2\) है, तो उसमें अलग-अलग अभाज्य गुणनखंड कितने हैं?
If a number has prime factorisation \(2^4\times3^7\times11^3\times13^2\), how many distinct prime factors does it have?
#distinct-prime-factors
#prime-exponents
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 4
B 16
C 7
D 5
Explanation opens after your attempt
Step 1
Concept
अलग-अलग अभाज्य गिनते समय केवल आधार गिने जाते हैं। / While counting distinct primes, only bases are counted.
Step 2
Why this answer is correct
आधार 2, 3, 11 और 13 हैं। / The bases are 2, 3, 11, and 13.
Step 3
Exam Tip
इसलिए अलग-अलग अभाज्य गुणनखंड 4 हैं। / Therefore, there are 4 distinct prime factors.
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यदि \(a=2^4\times3^5\times7\) और \(b=2^3\times3^2\times5\times7^2\), तो (ab) में 7 की घात क्या होगी?
If \(a=2^4\times3^5\times7\) and \(b=2^3\times3^2\times5\times7^2\), what will be the power of 7 in (ab)?
#product-factorisation
#powers
#hard
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? Hint Small clue
A 3
B 2
C 1
D 4
Explanation opens after your attempt
Step 1
Concept
गुणा में समान अभाज्य आधार की घातें जुड़ती हैं। / In multiplication, powers of the same prime base are added.
Step 2
Why this answer is correct
(a) में 7 की घात 1 है और (b) में 7 की घात 2 है। / The power of 7 in (a) is 1 and in (b) is 2.
Step 3
Exam Tip
(ab) में 7 की घात (1+2=3) होगी। / In (ab), the power of 7 will be (1+2=3).
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यदि \(x=2^7\times5^4\times11^2\) और \(y=2^2\times3^3\times5^3\times11\), तो (xy) में 11 की घात क्या होगी?
If \(x=2^7\times5^4\times11^2\) and \(y=2^2\times3^3\times5^3\times11\), what will be the power of 11 in (xy)?
#product-factorisation
#powers
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 3
B 2
C 1
D 4
Explanation opens after your attempt
Step 1
Concept
समान आधार 11 की घातें गुणा में जोड़ी जाती हैं। / Powers of the same base 11 are added in multiplication.
Step 2
Why this answer is correct
(x) में 11 की घात 2 है और (y) में 11 की घात 1 है। / The power of 11 in (x) is 2 and in (y) is 1.
Step 3
Exam Tip
कुल घात (2+1=3) होगी। / The total power will be (2+1=3).
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किस विकल्प में \(2^4\times3^2\times5\times7^2\) का सही मान है?
Which option gives the correct value of \(2^4\times3^2\times5\times7^2\)?
#evaluate-factorisation
#number-35280
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A 35280
B 17640
C 70560
D 22050
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\), \(3^2=9\) और \(7^2=49\) निकालें। / Calculate \(2^4=16\), \(3^2=9\), and \(7^2=49\).
Step 2
Why this answer is correct
\(16\times9\times5\times49=35280\)। / \(16\times9\times5\times49=35280\).
Step 3
Exam Tip
घातों को पहले अलग-अलग हल करें। / Solve powers separately first.
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किस विकल्प में \(2^8\times3^4\) का सही मान है?
Which option gives the correct value of \(2^8\times3^4\)?
#evaluate-factorisation
#number-20736
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A 20736
B 10368
C 41472
D 7776
Explanation opens after your attempt
Step 1
Concept
\(2^8=256\) और \(3^4=81\) निकालें। / Calculate \(2^8=256\) and \(3^4=81\).
Step 2
Why this answer is correct
\(256\times81=20736\)। / \(256\times81=20736\).
Step 3
Exam Tip
बड़ी घातों को अलग-अलग सरल करके गुणा करें। / Simplify higher powers separately and multiply.
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किस विकल्प में केवल अंतिम अभाज्य गुणनखंडन दिया गया है?
Which option gives only the final prime factorisation?
#prime-factorisation
#final-form
#hard
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? Hint Small clue
A \(2^3\times3^2\times5\times7\times11\)
B \(8\times9\times385\)
C \(2^3\times9\times385\)
D \(72\times385\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times7\times11\)
Step 1
Concept
अंतिम रूप में आधार अभाज्य होने चाहिए। / In the final form, bases must be prime.
Step 2
Why this answer is correct
पहले रूप में आधार 2, 3, 5, 7 और 11 अभाज्य हैं। / In the first form, the bases 2, 3, 5, 7, and 11 are prime.
Step 3
Exam Tip
8, 9, 385 और 72 संयुक्त हैं, इसलिए वे अंतिम रूप नहीं हैं। / 8, 9, 385, and 72 are composite, so they are not final forms.
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किस विकल्प में अभाज्य गुणनखंडन अधूरा है?
Which option has incomplete prime factorisation?
#prime-factorisation
#incomplete-form
#hard
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A \(2^4\times45\times49\)
B \(2^4\times3^2\times5\times7^2\)
C \(2^3\times3^3\times5\times7\)
D \(2\times3\times5^2\times7^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times45\times49\)
Step 1
Concept
अधूरे रूप में संयुक्त गुणनखंड बचा रहता है। / In an incomplete form, composite factors remain.
Step 2
Why this answer is correct
45 और 49 दोनों संयुक्त हैं। / Both 45 and 49 are composite.
Step 3
Exam Tip
\(2^4\times45\times49\) को \(2^4\times3^2\times5\times7^2\) में बदलना होगा। / \(2^4\times45\times49\) must be changed into \(2^4\times3^2\times5\times7^2\).
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यदि \(2^4\times3^2\times5\times7\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^4\times3^2\times5\times7\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#hard
#mcq
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A 5040
B 2520
C 10080
D 7560
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(3^2=9\) निकालें। / Calculate \(2^4=16\) and \(3^2=9\).
Step 2
Why this answer is correct
\(16\times9\times5\times7=5040\)। / \(16\times9\times5\times7=5040\).
Step 3
Exam Tip
घातों को पहले हल करने से सही विकल्प जल्दी मिलता है। / Solving powers first helps find the correct option quickly.
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यदि \(2^3\times5^2\times7^2\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^3\times5^2\times7^2\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#square-base
#hard
50 50-50 2 wrong hide
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A 9800
B 4900
C 19600
D 1225
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\), \(5^2=25\) और \(7^2=49\) निकालें। / Calculate \(2^3=8\), \(5^2=25\), and \(7^2=49\).
Step 2
Why this answer is correct
\(8\times25\times49=9800\)। / \(8\times25\times49=9800\).
Step 3
Exam Tip
तीनों घातों का मान अलग-अलग निकालें। / Find all three powers separately.
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संख्या 29400 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 29400?
#prime-factorisation
#number-29400
#hard
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A \(2^3\times3\times5^2\times7^2\)
B \(2^2\times3^2\times5^2\times7\)
C \(600\times49\)
D \(8\times3675\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times5^2\times7^2\)
Step 1
Concept
\(29400=600\times49\) लिखें। / Write \(29400=600\times49\).
Step 2
Why this answer is correct
\(600=2^3\times3\times5^2\) और \(49=7^2\), इसलिए \(29400=2^3\times3\times5^2\times7^2\)। / \(600=2^3\times3\times5^2\) and \(49=7^2\), so \(29400=2^3\times3\times5^2\times7^2\).
Step 3
Exam Tip
600 और 49 को पूरी तरह तोड़ें। / Break 600 and 49 completely.
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संख्या 33075 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 33075?
#prime-factorisation
#number-33075
#hard
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A \(3^3\times5^2\times7^2\)
B \(3^2\times5^3\times7^2\)
C \(675\times49\)
D \(27\times1225\)
Explanation opens after your attempt
Correct Answer
A. \(3^3\times5^2\times7^2\)
Step 1
Concept
\(33075=675\times49\) लिखें। / Write \(33075=675\times49\).
Step 2
Why this answer is correct
\(675=3^3\times5^2\) और \(49=7^2\), इसलिए \(33075=3^3\times5^2\times7^2\)। / \(675=3^3\times5^2\) and \(49=7^2\), so \(33075=3^3\times5^2\times7^2\).
Step 3
Exam Tip
675 और 49 को अभाज्य घातों में लिखें। / Write 675 and 49 as prime powers.
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संख्या 46656 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 46656?
#prime-factorisation
#number-46656
#hard
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A \(2^6\times3^6\)
B \(2^5\times3^6\)
C \(64\times729\)
D \(6^6\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^6\)
Step 1
Concept
\(46656=64\times729\) लिखा जा सकता है। / (46656) can be written as \(64\times729\).
Step 2
Why this answer is correct
\(64=2^6\) और \(729=3^6\), इसलिए \(46656=2^6\times3^6\)। / \(64=2^6\) and \(729=3^6\), so \(46656=2^6\times3^6\).
Step 3
Exam Tip
64 और 729 को अंतिम रूप में न छोड़ें। / Do not leave 64 and 729 in the final form.
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अभाज्य गुणनखंडन में \(600\times49\) को अंतिम उत्तर क्यों नहीं माना जाएगा?
Why will \(600\times49\) not be considered the final answer in prime factorisation?
#prime-factorisation
#concept-check
#hard
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A क्योंकि 600 और 49 संयुक्त रूप हैं / Because 600 and 49 are composite forms
B क्योंकि 49 अभाज्य संख्या है / Because 49 is prime
C क्योंकि 600 को तोड़ा नहीं जा सकता / Because 600 cannot be factorised
D क्योंकि गुणनफल बदल जाएगा / Because the product will change
Explanation opens after your attempt
Correct Answer
A. क्योंकि 600 और 49 संयुक्त रूप हैं / Because 600 and 49 are composite forms
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में हर आधार अभाज्य होना चाहिए। / In final prime factorisation, every base should be prime.
Step 2
Why this answer is correct
\(600=2^3\times3\times5^2\) और \(49=7^2\) है। / \(600=2^3\times3\times5^2\) and \(49=7^2\).
Step 3
Exam Tip
इसलिए अंतिम रूप \(2^3\times3\times5^2\times7^2\) होगा। / Therefore, the final form is \(2^3\times3\times5^2\times7^2\).
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अभाज्य गुणनखंडन में \(36^2\times7\) को अंतिम रूप क्यों नहीं माना जाता?
Why is \(36^2\times7\) not considered the final form in prime factorisation?
#prime-factorisation
#composite-base
#hard
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A क्योंकि 36 संयुक्त संख्या है / Because 36 is composite
B क्योंकि 7 संयुक्त संख्या है / Because 7 is composite
C क्योंकि घात लिखना हमेशा गलत है / Because writing powers is always wrong
D क्योंकि गुणन का प्रयोग नहीं किया जाता / Because multiplication is not used
Explanation opens after your attempt
Correct Answer
A. क्योंकि 36 संयुक्त संख्या है / Because 36 is composite
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में आधार अभाज्य होने चाहिए। / In final prime factorisation, the bases should be prime.
Step 2
Why this answer is correct
\(36=2^2\times3^2\), इसलिए \(36^2\) को \(2^4\times3^4\) में बदलना होगा। / \(36=2^2\times3^2\), so \(36^2\) must be changed into \(2^4\times3^4\).
Step 3
Exam Tip
अंतिम उत्तर में 36 जैसा संयुक्त आधार न रखें। / Do not keep a composite base like 36 in the final answer.
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संख्या 5544 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 5544?
#prime-factorisation
#number-5544
#hard
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A \(2^3\times3^2\times7\times11\)
B \(2^2\times3^3\times7\times11\)
C \(8\times693\)
D \(2^3\times9\times77\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times7\times11\)
Step 1
Concept
\(5544=8\times693\) लिखें। / Write \(5544=8\times693\).
Step 2
Why this answer is correct
\(8=2^3\) और \(693=3^2\times7\times11\), इसलिए \(5544=2^3\times3^2\times7\times11\)। / \(8=2^3\) and \(693=3^2\times7\times11\), so \(5544=2^3\times3^2\times7\times11\).
Step 3
Exam Tip
693 को अंतिम रूप में न छोड़ें। / Do not leave 693 in the final form.
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संख्या 6048 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 6048?
#prime-factorisation
#number-6048
#hard
50 50-50 2 wrong hide
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A \(2^5\times3^3\times7\)
B \(2^4\times3^3\times7\)
C \(32\times189\)
D \(2^5\times27\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^3\times7\)
Step 1
Concept
\(6048=32\times189\) लिखें। / Write \(6048=32\times189\).
Step 2
Why this answer is correct
\(32=2^5\) और \(189=3^3\times7\), इसलिए \(6048=2^5\times3^3\times7\)। / \(32=2^5\) and \(189=3^3\times7\), so \(6048=2^5\times3^3\times7\).
Step 3
Exam Tip
189 को \(3^3\times7\) में बदलें। / Change 189 into \(3^3\times7\).
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संख्या 6930 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 6930?
#prime-factorisation
#number-6930
#hard
50 50-50 2 wrong hide
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A \(2\times3^2\times5\times7\times11\)
B \(2^2\times3\times5\times7\times11\)
C \(63\times110\)
D \(2\times9\times385\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\times7\times11\)
Step 1
Concept
\(6930=63\times110\) लिखें। / Write \(6930=63\times110\).
Step 2
Why this answer is correct
\(63=3^2\times7\) और \(110=2\times5\times11\), इसलिए \(6930=2\times3^2\times5\times7\times11\)। / \(63=3^2\times7\) and \(110=2\times5\times11\), so \(6930=2\times3^2\times5\times7\times11\).
Step 3
Exam Tip
63 और 110 दोनों को अभाज्य रूप दें। / Give prime form to both 63 and 110.
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संख्या 8316 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 8316?
#prime-factorisation
#number-8316
#hard
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A \(2^2\times3^3\times7\times11\)
B \(2^3\times3^2\times7\times11\)
C \(4\times2079\)
D \(36\times231\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\times7\times11\)
Step 1
Concept
\(8316=36\times231\) लिखें। / Write \(8316=36\times231\).
Step 2
Why this answer is correct
\(36=2^2\times3^2\) और \(231=3\times7\times11\), इसलिए \(8316=2^2\times3^3\times7\times11\)। / \(36=2^2\times3^2\) and \(231=3\times7\times11\), so \(8316=2^2\times3^3\times7\times11\).
Step 3
Exam Tip
3 की कुल घात 3 बनती है। / The total power of 3 becomes 3.
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संख्या 9240 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 9240?
#prime-factorisation
#number-9240
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^3\times3\times5\times7\times11\)
B \(2^2\times3\times5\times7\times11\)
C \(8\times1155\)
D \(2^3\times105\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times5\times7\times11\)
Step 1
Concept
\(9240=8\times1155\) लिखें। / Write \(9240=8\times1155\).
Step 2
Why this answer is correct
\(8=2^3\) और \(1155=3\times5\times7\times11\), इसलिए \(9240=2^3\times3\times5\times7\times11\)। / \(8=2^3\) and \(1155=3\times5\times7\times11\), so \(9240=2^3\times3\times5\times7\times11\).
Step 3
Exam Tip
1155 को पूरा अभाज्य रूप दें। / Give 1155 its complete prime form.
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संख्या 10395 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 10395?
#prime-factorisation
#number-10395
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(3^3\times5\times7\times11\)
B \(3^2\times5\times7\times11\)
C \(27\times385\)
D \(135\times77\)
Explanation opens after your attempt
Correct Answer
A. \(3^3\times5\times7\times11\)
Step 1
Concept
\(10395=27\times385\) लिखें। / Write \(10395=27\times385\).
Step 2
Why this answer is correct
\(27=3^3\) और \(385=5\times7\times11\), इसलिए \(10395=3^3\times5\times7\times11\)। / \(27=3^3\) and \(385=5\times7\times11\), so \(10395=3^3\times5\times7\times11\).
Step 3
Exam Tip
385 को भी अभाज्य रूप में तोड़ें। / Break 385 into prime form too.
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संख्या 11025 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 11025?
#prime-factorisation
#square-number
#hard
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? Hint Small clue
A \(3^2\times5^2\times7^2\)
B \(3^3\times5^2\times7\)
C \(105\times105\)
D \(9\times1225\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5^2\times7^2\)
Step 1
Concept
\(11025=105^2\) पहचाना जा सकता है। / Recognise \(11025=105^2\).
Step 2
Why this answer is correct
\(105=3\times5\times7\), इसलिए \(11025=3^2\times5^2\times7^2\)। / Since \(105=3\times5\times7\), \(11025=3^2\times5^2\times7^2\).
Step 3
Exam Tip
वर्ग संख्या में अभाज्य घातें सम आती हैं। / In a square number, prime exponents are even.
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संख्या 11760 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 11760?
#prime-factorisation
#number-11760
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^4\times3\times5\times7^2\)
B \(2^3\times3^2\times5\times7\)
C \(16\times735\)
D \(2^4\times15\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3\times5\times7^2\)
Step 1
Concept
\(11760=16\times735\) लिखें। / Write \(11760=16\times735\).
Step 2
Why this answer is correct
\(16=2^4\) और \(735=3\times5\times7^2\), इसलिए \(11760=2^4\times3\times5\times7^2\)। / \(16=2^4\) and \(735=3\times5\times7^2\), so \(11760=2^4\times3\times5\times7^2\).
Step 3
Exam Tip
735 को पूरा अभाज्य रूप दें। / Give 735 its complete prime form.
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संख्या 14112 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 14112?
#prime-factorisation
#number-14112
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^5\times3^2\times7^2\)
B \(2^4\times3^3\times7^2\)
C \(32\times441\)
D \(2^5\times21^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^2\times7^2\)
Step 1
Concept
\(14112=32\times441\) लिखें। / Write \(14112=32\times441\).
Step 2
Why this answer is correct
\(32=2^5\) और \(441=3^2\times7^2\), इसलिए \(14112=2^5\times3^2\times7^2\)। / \(32=2^5\) and \(441=3^2\times7^2\), so \(14112=2^5\times3^2\times7^2\).
Step 3
Exam Tip
441 को \(3^2\times7^2\) में बदलें। / Change 441 into \(3^2\times7^2\).
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संख्या 15120 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 15120?
#prime-factorisation
#number-15120
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^4\times3^3\times5\times7\)
B \(2^3\times3^3\times5\times7\)
C \(16\times945\)
D \(2^4\times27\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^3\times5\times7\)
Step 1
Concept
\(15120=16\times945\) लिखें। / Write \(15120=16\times945\).
Step 2
Why this answer is correct
\(16=2^4\) और \(945=3^3\times5\times7\), इसलिए \(15120=2^4\times3^3\times5\times7\)। / \(16=2^4\) and \(945=3^3\times5\times7\), so \(15120=2^4\times3^3\times5\times7\).
Step 3
Exam Tip
945 को अंतिम रूप में न छोड़ें। / Do not leave 945 in the final form.
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संख्या 16632 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 16632?
#prime-factorisation
#number-16632
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2^3\times3^3\times7\times11\)
B \(2^2\times3^4\times7\times11\)
C \(8\times2079\)
D \(2^3\times27\times77\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times7\times11\)
Step 1
Concept
\(16632=8\times2079\) लिखें। / Write \(16632=8\times2079\).
Step 2
Why this answer is correct
\(2079=3^3\times7\times11\), इसलिए \(16632=2^3\times3^3\times7\times11\)। / \(2079=3^3\times7\times11\), so \(16632=2^3\times3^3\times7\times11\).
Step 3
Exam Tip
2079 को अभाज्य गुणनखंडों तक तोड़ें। / Break 2079 down to prime factors.
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संख्या 17640 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 17640?
#prime-factorisation
#number-17640
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2^3\times3^2\times5\times7^2\)
B \(2^4\times3^2\times5\times7\)
C \(8\times2205\)
D \(2^3\times45\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times7^2\)
Step 1
Concept
\(17640=8\times2205\) लिखें। / Write \(17640=8\times2205\).
Step 2
Why this answer is correct
\(2205=3^2\times5\times7^2\), इसलिए \(17640=2^3\times3^2\times5\times7^2\)। / \(2205=3^2\times5\times7^2\), so \(17640=2^3\times3^2\times5\times7^2\).
Step 3
Exam Tip
2205 को पूरा अभाज्य रूप दें। / Give 2205 its complete prime form.
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संख्या 19600 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 19600?
#prime-factorisation
#square-number
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^4\times5^2\times7^2\)
B \(2^3\times5^2\times7^2\)
C \(140\times140\)
D \(16\times1225\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times5^2\times7^2\)
Step 1
Concept
\(19600=140^2\) पहचाना जा सकता है। / Recognise \(19600=140^2\).
Step 2
Why this answer is correct
\(140=2^2\times5\times7\), इसलिए \(19600=2^4\times5^2\times7^2\)। / Since \(140=2^2\times5\times7\), \(19600=2^4\times5^2\times7^2\).
Step 3
Exam Tip
वर्ग संख्या में घातों की समता जांचें। / Check evenness of exponents in square numbers.
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संख्या 20790 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 20790?
#prime-factorisation
#number-20790
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2\times3^3\times5\times7\times11\)
B \(2^2\times3^2\times5\times7\times11\)
C \(54\times385\)
D \(2\times27\times385\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^3\times5\times7\times11\)
Step 1
Concept
\(20790=54\times385\) लिखें। / Write \(20790=54\times385\).
Step 2
Why this answer is correct
\(54=2\times3^3\) और \(385=5\times7\times11\), इसलिए \(20790=2\times3^3\times5\times7\times11\)। / \(54=2\times3^3\) and \(385=5\times7\times11\), so \(20790=2\times3^3\times5\times7\times11\).
Step 3
Exam Tip
54 और 385 दोनों को पूरा तोड़ें। / Break both 54 and 385 completely.
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संख्या 21168 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 21168?
#prime-factorisation
#number-21168
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^4\times3^3\times7^2\)
B \(2^5\times3^2\times7^2\)
C \(16\times1323\)
D \(2^4\times27\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^3\times7^2\)
Step 1
Concept
\(21168=16\times1323\) लिखें। / Write \(21168=16\times1323\).
Step 2
Why this answer is correct
\(1323=3^3\times7^2\), इसलिए \(21168=2^4\times3^3\times7^2\)। / \(1323=3^3\times7^2\), so \(21168=2^4\times3^3\times7^2\).
Step 3
Exam Tip
1323 को 3 और 7 की घातों में बदलें। / Convert 1323 into powers of 3 and 7.
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संख्या 24255 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 24255?
#prime-factorisation
#number-24255
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(3^2\times5\times7^2\times11\)
B \(3^3\times5\times7\times11\)
C \(45\times539\)
D \(9\times2695\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5\times7^2\times11\)
Step 1
Concept
\(24255=45\times539\) लिखें। / Write \(24255=45\times539\).
Step 2
Why this answer is correct
\(45=3^2\times5\) और \(539=7^2\times11\), इसलिए \(24255=3^2\times5\times7^2\times11\)। / \(45=3^2\times5\) and \(539=7^2\times11\), so \(24255=3^2\times5\times7^2\times11\).
Step 3
Exam Tip
539 को भी अभाज्य रूप दें। / Give 539 its prime form too.
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संख्या 27720 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 27720?
#prime-factorisation
#number-27720
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^3\times3^2\times5\times7\times11\)
B \(2^2\times3^3\times5\times7\times11\)
C \(8\times3465\)
D \(2^3\times9\times385\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times7\times11\)
Step 1
Concept
\(27720=8\times3465\) लिखें। / Write \(27720=8\times3465\).
Step 2
Why this answer is correct
\(3465=3^2\times5\times7\times11\), इसलिए \(27720=2^3\times3^2\times5\times7\times11\)। / \(3465=3^2\times5\times7\times11\), so \(27720=2^3\times3^2\times5\times7\times11\).
Step 3
Exam Tip
3465 को पूरी तरह तोड़ें। / Break 3465 completely.
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संख्या 28224 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 28224?
#prime-factorisation
#number-28224
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^6\times3^2\times7^2\)
B \(2^5\times3^3\times7^2\)
C \(64\times441\)
D \(2^6\times21^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^2\times7^2\)
Step 1
Concept
\(28224=64\times441\) लिखें। / Write \(28224=64\times441\).
Step 2
Why this answer is correct
\(64=2^6\) और \(441=3^2\times7^2\), इसलिए \(28224=2^6\times3^2\times7^2\)। / \(64=2^6\) and \(441=3^2\times7^2\), so \(28224=2^6\times3^2\times7^2\).
Step 3
Exam Tip
441 को अभाज्य घातों में लिखें। / Write 441 as prime powers.
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संख्या 31104 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 31104?
#prime-factorisation
#number-31104
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^7\times3^5\)
B \(2^6\times3^5\)
C \(128\times243\)
D \(2^7\times81\times3\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^5\)
Step 1
Concept
\(31104=128\times243\) लिखें। / Write \(31104=128\times243\).
Step 2
Why this answer is correct
\(128=2^7\) और \(243=3^5\), इसलिए \(31104=2^7\times3^5\)। / \(128=2^7\) and \(243=3^5\), so \(31104=2^7\times3^5\).
Step 3
Exam Tip
128 और 243 संयुक्त हैं, इसलिए अभाज्य आधार रखें। / 128 and 243 are composite, so keep prime bases.
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संख्या 35280 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 35280?
#prime-factorisation
#number-35280
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^4\times3^2\times5\times7^2\)
B \(2^3\times3^3\times5\times7^2\)
C \(16\times2205\)
D \(2^4\times45\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^2\times5\times7^2\)
Step 1
Concept
\(35280=16\times2205\) लिखें। / Write \(35280=16\times2205\).
Step 2
Why this answer is correct
\(2205=3^2\times5\times7^2\), इसलिए \(35280=2^4\times3^2\times5\times7^2\)। / \(2205=3^2\times5\times7^2\), so \(35280=2^4\times3^2\times5\times7^2\).
Step 3
Exam Tip
2205 को पूरा अभाज्य रूप दें। / Give 2205 its complete prime form.
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यदि \(27720=2^a\times3^2\times5\times7\times11\), तो (a) का मान क्या है?
If \(27720=2^a\times3^2\times5\times7\times11\), what is the value of (a)?
#exponent-comparison
#number-27720
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 3
B 2
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
\(27720=8\times3465\) है। / \(27720=8\times3465\).
Step 2
Why this answer is correct
\(8=2^3\) और \(3465=3^2\times5\times7\times11\), इसलिए 2 की घात 3 है। / \(8=2^3\) and \(3465=3^2\times5\times7\times11\), so the power of 2 is 3.
Step 3
Exam Tip
तुलना करने पर (a=3) है। / Comparing gives (a=3).
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यदि \(31104=2^7\times3^b\), तो (b) का मान क्या है?
If \(31104=2^7\times3^b\), what is the value of (b)?
#exponent-comparison
#number-31104
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 5
B 4
C 6
D 7
Explanation opens after your attempt
Step 1
Concept
\(31104=128\times243\) लिखें। / Write \(31104=128\times243\).
Step 2
Why this answer is correct
\(128=2^7\) और \(243=3^5\), इसलिए \(31104=2^7\times3^5\)। / \(128=2^7\) and \(243=3^5\), so \(31104=2^7\times3^5\).
Step 3
Exam Tip
दिए गए रूप से तुलना करने पर (b=5) है। / Comparing with the given form gives (b=5).
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यदि \(19600=2^4\times5^m\times7^2\), तो (m) का मान क्या है?
If \(19600=2^4\times5^m\times7^2\), what is the value of (m)?
#exponent-comparison
#square-number
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
\(19600=140^2\) है। / \(19600=140^2\).
Step 2
Why this answer is correct
\(140=2^2\times5\times7\), इसलिए \(19600=2^4\times5^2\times7^2\)। / \(140=2^2\times5\times7\), so \(19600=2^4\times5^2\times7^2\).
Step 3
Exam Tip
तुलना करने पर (m=2) होगा। / Comparing gives (m=2).
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यदि \(20790=2\times3^p\times5\times7\times11\), तो (p) का मान क्या है?
If \(20790=2\times3^p\times5\times7\times11\), what is the value of (p)?
#exponent-comparison
#number-20790
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 3
B 2
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
\(20790=54\times385\) लिखें। / Write \(20790=54\times385\).
Step 2
Why this answer is correct
\(54=2\times3^3\) और \(385=5\times7\times11\), इसलिए 3 की घात 3 है। / \(54=2\times3^3\) and \(385=5\times7\times11\), so the power of 3 is 3.
Step 3
Exam Tip
तुलना करने पर (p=3) मिलेगा। / Comparing gives (p=3).
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times3^2\times7\times11\) है?
Which number has prime factorisation \(2^3\times3^2\times7\times11\)?
#evaluate-factorisation
#number-5544
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 5544
B 2772
C 11088
D 8316
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) और \(3^2=9\) निकालें। / Calculate \(2^3=8\) and \(3^2=9\).
Step 2
Why this answer is correct
\(8\times9\times7\times11=5544\)। / \(8\times9\times7\times11=5544\).
Step 3
Exam Tip
घातों को पहले सरल करके गुणा करें। / Simplify powers first and then multiply.
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किस संख्या का अभाज्य गुणनखंडन \(2^5\times3^3\times7\) है?
Which number has prime factorisation \(2^5\times3^3\times7\)?
#evaluate-factorisation
#number-6048
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 6048
B 3024
C 12096
D 8064
Explanation opens after your attempt
Step 1
Concept
\(2^5=32\) और \(3^3=27\) निकालें। / Calculate \(2^5=32\) and \(3^3=27\).
Step 2
Why this answer is correct
\(32\times27\times7=6048\)। / \(32\times27\times7=6048\).
Step 3
Exam Tip
बड़ी घातों का मान अलग से निकालें। / Find the values of higher powers separately.
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किस संख्या का अभाज्य गुणनखंडन \(3^2\times5^2\times7^2\) है?
Which number has prime factorisation \(3^2\times5^2\times7^2\)?
#evaluate-factorisation
#square-number
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 11025
B 3675
C 22050
D 1225
Explanation opens after your attempt
Step 1
Concept
\(3^2=9\), \(5^2=25\) और \(7^2=49\) निकालें। / Calculate \(3^2=9\), \(5^2=25\), and \(7^2=49\).
Step 2
Why this answer is correct
\(9\times25\times49=11025\)। / \(9\times25\times49=11025\).
Step 3
Exam Tip
वर्ग रूप में सभी घातें 2 हैं, इसलिए गुणा ध्यान से करें। / In this square form, all exponents are 2, so multiply carefully.
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किस संख्या का अभाज्य गुणनखंडन \(2^4\times3\times5\times7^2\) है?
Which number has prime factorisation \(2^4\times3\times5\times7^2\)?
#evaluate-factorisation
#number-11760
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 11760
B 5880
C 23520
D 17640
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(7^2=49\) निकालें। / Calculate \(2^4=16\) and \(7^2=49\).
Step 2
Why this answer is correct
\(16\times3\times5\times49=11760\)। / \(16\times3\times5\times49=11760\).
Step 3
Exam Tip
घातों का मान पहले निकालने से गणना आसान होती है। / Calculating powers first makes the work easier.
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किस संख्या का अभाज्य गुणनखंडन \(2^7\times3^5\) है?
Which number has prime factorisation \(2^7\times3^5\)?
#evaluate-factorisation
#number-31104
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 31104
B 15552
C 62208
D 20736
Explanation opens after your attempt
Step 1
Concept
\(2^7=128\) और \(3^5=243\) निकालें। / Calculate \(2^7=128\) and \(3^5=243\).
Step 2
Why this answer is correct
\(128\times243=31104\)। / \(128\times243=31104\).
Step 3
Exam Tip
दोनों घातों को पहले सरल करना सही तरीका है। / Simplifying both powers first is the correct method.
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यदि संख्या \(2^5\times3^4\times5^2\times7\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^5\times3^4\times5^2\times7\), by which smallest number should it be multiplied to make a perfect square?
#perfect-square
#prime-exponents
#hard
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A 14
B 7
C 2
D 28
Explanation opens after your attempt
Step 1
Concept
पूर्ण वर्ग के लिए सभी घातें सम होनी चाहिए। / For a perfect square, all exponents must be even.
Step 2
Why this answer is correct
2 की घात 5 और 7 की घात 1 विषम हैं। / The powers of 2 and 7 are odd.
Step 3
Exam Tip
\(2\times7=14\) से गुणा करने पर सभी घातें सम हो जाएंगी। / Multiplying by \(2\times7=14\) makes all exponents even.
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यदि संख्या \(2^4\times3^5\times5^2\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^4\times3^5\times5^2\), by which smallest number should it be divided to make a perfect square?
#perfect-square
#division
#hard
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A 3
B 9
C 15
D 5
Explanation opens after your attempt
Step 1
Concept
पूर्ण वर्ग में सभी घातें सम होती हैं। / In a perfect square, all exponents are even.
Step 2
Why this answer is correct
केवल 3 की घात 5 विषम है। / Only the power of 3 is odd.
Step 3
Exam Tip
3 से भाग देने पर घात 4 हो जाएगी और संख्या पूर्ण वर्ग बन जाएगी। / Dividing by 3 makes the power 4 and the number becomes a perfect square.
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यदि संख्या \(2^4\times3^2\times5^3\times7\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^4\times3^2\times5^3\times7\), by which smallest number should it be multiplied to make a perfect cube?
#perfect-cube
#prime-exponents
#hard
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A 588
B 147
C 84
D 441
Explanation opens after your attempt
Step 1
Concept
पूर्ण घन में हर घात 3 का गुणज होनी चाहिए। / In a perfect cube, every exponent must be a multiple of 3.
Step 2
Why this answer is correct
2 की घात 4 को 6, 3 की घात 2 को 3 और 7 की घात 1 को 3 बनाना होगा। / Powers 4, 2, and 1 must become 6, 3, and 3 respectively.
Step 3
Exam Tip
गुणक \(2^2\times3\times7^2=588\) होगा। / The multiplier is \(2^2\times3\times7^2=588\).
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यदि संख्या \(2^8\times3^5\times5^4\times11^2\) है, तो इसे पूर्ण घन बनाने के लिए किस सबसे छोटी संख्या से भाग देना होगा?
If the number is \(2^8\times3^5\times5^4\times11^2\), by which smallest number should it be divided to make a perfect cube?
#perfect-cube
#division
#hard
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A \(2^2\times3^2\times5\times11^2\)
B \(2\times3\times5^2\times11\)
C \(2^2\times3\times5\times11\)
D \(3^2\times5^2\times11^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times5\times11^2\)
Step 1
Concept
पूर्ण घन के लिए घातें 3 के गुणज चाहिए। / For a perfect cube, exponents should be multiples of 3.
Step 2
Why this answer is correct
8 को 6, 5 को 3, 4 को 3 और 2 को 0 तक घटाना सबसे छोटा तरीका है। / Reduce 8 to 6, 5 to 3, 4 to 3, and 2 to 0 for the smallest divisor.
Step 3
Exam Tip
इसलिए भाजक \(2^2\times3^2\times5\times11^2\) है। / So the divisor is \(2^2\times3^2\times5\times11^2\).
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यदि \(n=2^6\times3^4\times5^2\times7\), तो (n) किस संख्या से विभाज्य नहीं होगा?
If \(n=2^6\times3^4\times5^2\times7\), by which number will (n) not be divisible?
#divisibility
#prime-exponents
#hard
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A \(3^5\)
B \(2^5\times3^4\)
C \(2^6\times5^2\times7\)
D \(3^2\times5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(3^5\)
Step 1
Concept
किसी भाजक के लिए उसकी हर अभाज्य घात संख्या में पर्याप्त होनी चाहिए। / For divisibility, every prime power of the divisor must be available in the number.
Step 2
Why this answer is correct
(n) में 3 की घात 4 है, पर \(3^5\) के लिए घात 5 चाहिए। / (n) has power 4 of 3, but \(3^5\) needs power 5.
Step 3
Exam Tip
इसलिए (n), \(3^5\) से विभाज्य नहीं होगा। / Therefore, (n) is not divisible by \(3^5\).
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यदि \(n=2^8\times3^3\times5^5\), तो (n) किस संख्या से अवश्य विभाज्य होगा?
If \(n=2^8\times3^3\times5^5\), by which number must (n) be divisible?
#divisibility
#prime-exponents
#hard
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A \(2^7\times3^2\times5^4\)
B \(2^9\times3^2\)
C \(3^4\times5\)
D \(2^8\times5^6\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^2\times5^4\)
Step 1
Concept
भाज्य होने के लिए भाजक की हर घात दी गई संख्या में बराबर या कम होनी चाहिए। / For divisibility, each exponent in the divisor must be less than or equal to the corresponding exponent in the number.
Step 2
Why this answer is correct
\(2^7\), \(3^2\) और \(5^4\) सभी (n) में उपलब्ध हैं। / \(2^7\), \(3^2\), and \(5^4\) are all available in (n).
Step 3
Exam Tip
इसलिए (n), \(2^7\times3^2\times5^4\) से अवश्य विभाज्य होगा। / Therefore, (n) must be divisible by \(2^7\times3^2\times5^4\).
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4\times3^2\times5^2\times7^2\) है, तो उसके कुल अभाज्य गुणनखंडों की संख्या कितनी है, यदि दोहराव गिना जाए?
If a number has prime factorisation \(2^4\times3^2\times5^2\times7^2\), how many prime factors does it have if repetition is counted?
#counting-prime-factors
#prime-exponents
#hard
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A 10
B 4
C 8
D 12
Explanation opens after your attempt
Step 1
Concept
दोहराव सहित गिनने के लिए घातों को जोड़ते हैं। / To count with repetition, add the exponents.
Step 2
Why this answer is correct
(4+2+2+2=10)। / (4+2+2+2=10).
Step 3
Exam Tip
अलग-अलग अभाज्य गिनने और दोहराव सहित गिनने में अंतर रखें। / Keep the difference between distinct prime count and repeated prime count clear.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^7\times3^5\times11^2\times13\) है, तो उसमें अलग-अलग अभाज्य गुणनखंड कितने हैं?
If a number has prime factorisation \(2^7\times3^5\times11^2\times13\), how many distinct prime factors does it have?
#distinct-prime-factors
#prime-exponents
#hard
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A 4
B 15
C 7
D 5
Explanation opens after your attempt
Step 1
Concept
अलग-अलग अभाज्य गुणनखंड गिनते समय घात नहीं जोड़ते। / While counting distinct prime factors, do not add exponents.
Step 2
Why this answer is correct
अभाज्य आधार 2, 3, 11 और 13 हैं। / The prime bases are 2, 3, 11, and 13.
Step 3
Exam Tip
इसलिए अलग-अलग अभाज्य गुणनखंडों की संख्या 4 है। / Therefore, the number of distinct prime factors is 4.
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यदि \(a=2^5\times3^2\times7\) और \(b=2^3\times3^4\times5\), तो (ab) में 3 की घात क्या होगी?
If \(a=2^5\times3^2\times7\) and \(b=2^3\times3^4\times5\), what will be the power of 3 in (ab)?
#product-factorisation
#powers
#hard
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A 6
B 4
C 2
D 8
Explanation opens after your attempt
Step 1
Concept
गुणा में समान अभाज्य आधार की घातें जुड़ती हैं। / In multiplication, powers of the same prime base are added.
Step 2
Why this answer is correct
(a) में 3 की घात 2 है और (b) में 3 की घात 4 है। / The power of 3 in (a) is 2 and in (b) is 4.
Step 3
Exam Tip
(ab) में 3 की घात (2+4=6) होगी। / In (ab), the power of 3 will be (2+4=6).
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यदि \(x=2^8\times5^3\times11\) और \(y=2^4\times3^2\times5^5\), तो (xy) में 5 की घात क्या होगी?
If \(x=2^8\times5^3\times11\) and \(y=2^4\times3^2\times5^5\), what will be the power of 5 in (xy)?
#product-factorisation
#powers
#hard
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A 8
B 5
C 3
D 10
Explanation opens after your attempt
Step 1
Concept
समान आधार 5 की घातें गुणा में जुड़ेंगी। / Powers with the same base 5 are added in multiplication.
Step 2
Why this answer is correct
(x) में 5 की घात 3 है और (y) में 5 की घात 5 है। / The power of 5 in (x) is 3 and in (y) is 5.
Step 3
Exam Tip
कुल घात (3+5=8) होगी। / The total power will be (3+5=8).
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किस विकल्प में \(2^4\times3^3\times7^2\) का सही मान है?
Which option gives the correct value of \(2^4\times3^3\times7^2\)?
#evaluate-factorisation
#number-21168
#hard
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A 21168
B 10584
C 28224
D 14112
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\), \(3^3=27\) और \(7^2=49\) निकालें। / Calculate \(2^4=16\), \(3^3=27\), and \(7^2=49\).
Step 2
Why this answer is correct
\(16\times27\times49=21168\)। / \(16\times27\times49=21168\).
Step 3
Exam Tip
तीनों घातों को पहले अलग-अलग हल करें। / Solve all three powers separately first.
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किस विकल्प में \(2^6\times3^2\times7^2\) का सही मान है?
Which option gives the correct value of \(2^6\times3^2\times7^2\)?
#evaluate-factorisation
#number-28224
#hard
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A 28224
B 14112
C 56448
D 21168
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\), \(3^2=9\) और \(7^2=49\) निकालें। / Calculate \(2^6=64\), \(3^2=9\), and \(7^2=49\).
Step 2
Why this answer is correct
\(64\times9\times49=28224\)। / \(64\times9\times49=28224\).
Step 3
Exam Tip
गुणा को चरणों में करें ताकि गलती न हो। / Do multiplication step by step to avoid mistakes.
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किस विकल्प में केवल अंतिम अभाज्य गुणनखंडन दिया गया है?
Which option gives only the final prime factorisation?
#prime-factorisation
#final-form
#hard
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A \(2^4\times3^2\times5\times7^2\)
B \(16\times45\times49\)
C \(2^4\times45\times49\)
D \(8\times4410\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^2\times5\times7^2\)
Step 1
Concept
अंतिम रूप में आधार अभाज्य होने चाहिए। / In the final form, bases must be prime.
Step 2
Why this answer is correct
पहले विकल्प में आधार 2, 3, 5 और 7 हैं, जो अभाज्य हैं। / In the first option, bases 2, 3, 5, and 7 are prime.
Step 3
Exam Tip
16, 45, 49 और 4410 संयुक्त हैं, इसलिए वे अंतिम रूप नहीं हैं। / 16, 45, 49, and 4410 are composite, so they are not final forms.
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किस विकल्प में अभाज्य गुणनखंडन अधूरा है?
Which option has incomplete prime factorisation?
#prime-factorisation
#incomplete-form
#hard
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A \(2^5\times21^2\)
B \(2^5\times3^2\times7^2\)
C \(2^3\times3^2\times5\times7\times11\)
D \(3^2\times5^2\times7^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times21^2\)
Step 1
Concept
अधूरे रूप में कोई संयुक्त आधार बचा रहता है। / In an incomplete form, a composite base remains.
Step 2
Why this answer is correct
21 संयुक्त है और \(21=3\times7\), इसलिए \(2^5\times21^2\) अंतिम नहीं है। / 21 is composite and \(21=3\times7\), so \(2^5\times21^2\) is not final.
Step 3
Exam Tip
इसे \(2^5\times3^2\times7^2\) में बदलें। / Change it into \(2^5\times3^2\times7^2\).
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यदि \(2^6\times3^2\times7^2\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^6\times3^2\times7^2\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#hard
#mcq
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A 28224
B 14112
C 56448
D 21168
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\), \(3^2=9\) और \(7^2=49\) हैं। / \(2^6=64\), \(3^2=9\), and \(7^2=49\).
Step 2
Why this answer is correct
\(64\times9\times49=28224\)। / \(64\times9\times49=28224\).
Step 3
Exam Tip
घातों को पहले हल करने से सही विकल्प जल्दी मिलता है। / Solving powers first helps find the correct option quickly.
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यदि \(2^4\times5^2\times7^2\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^4\times5^2\times7^2\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#square-number
#hard
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A 19600
B 9800
C 39200
D 4900
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\), \(5^2=25\) और \(7^2=49\) निकालें। / Calculate \(2^4=16\), \(5^2=25\), and \(7^2=49\).
Step 2
Why this answer is correct
\(16\times25\times49=19600\)। / \(16\times25\times49=19600\).
Step 3
Exam Tip
तीनों घातों का मान अलग-अलग निकालना सुरक्षित रहता है। / Finding all three powers separately is safer.
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संख्या 39200 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 39200?
#prime-factorisation
#number-39200
#hard
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A \(2^5\times5^2\times7^2\)
B \(2^4\times5^2\times7^2\)
C \(32\times1225\)
D \(2^5\times35^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times5^2\times7^2\)
Step 1
Concept
\(39200=32\times1225\) लिखें। / Write \(39200=32\times1225\).
Step 2
Why this answer is correct
\(32=2^5\) और \(1225=5^2\times7^2\), इसलिए \(39200=2^5\times5^2\times7^2\)। / \(32=2^5\) and \(1225=5^2\times7^2\), so \(39200=2^5\times5^2\times7^2\).
Step 3
Exam Tip
1225 को अभाज्य घातों में बदलें। / Convert 1225 into prime powers.
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संख्या 41580 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 41580?
#prime-factorisation
#number-41580
#hard
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A \(2^2\times3^3\times5\times7\times11\)
B \(2\times3^3\times5\times7\times11\)
C \(4\times10395\)
D \(36\times1155\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\times5\times7\times11\)
Step 1
Concept
\(41580=4\times10395\) लिखें। / Write \(41580=4\times10395\).
Step 2
Why this answer is correct
\(10395=3^3\times5\times7\times11\), इसलिए \(41580=2^2\times3^3\times5\times7\times11\)। / \(10395=3^3\times5\times7\times11\), so \(41580=2^2\times3^3\times5\times7\times11\).
Step 3
Exam Tip
10395 को पूरा अभाज्य रूप दें। / Give 10395 its complete prime form.
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संख्या 62208 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 62208?
#prime-factorisation
#number-62208
#hard
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A \(2^8\times3^5\)
B \(2^7\times3^5\)
C \(256\times243\)
D \(2^8\times81\times3\)
Explanation opens after your attempt
Correct Answer
A. \(2^8\times3^5\)
Step 1
Concept
\(62208=256\times243\) लिखें। / Write \(62208=256\times243\).
Step 2
Why this answer is correct
\(256=2^8\) और \(243=3^5\), इसलिए \(62208=2^8\times3^5\)। / \(256=2^8\) and \(243=3^5\), so \(62208=2^8\times3^5\).
Step 3
Exam Tip
256 और 243 को अभाज्य घातों में लिखें। / Write 256 and 243 as prime powers.
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अभाज्य गुणनखंडन में \(8\times3465\) को अंतिम उत्तर क्यों नहीं माना जाएगा?
Why will \(8\times3465\) not be considered the final answer in prime factorisation?
#prime-factorisation
#concept-check
#hard
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A क्योंकि 8 और 3465 संयुक्त रूप हैं / Because 8 and 3465 are composite forms
B क्योंकि 8 अभाज्य है / Because 8 is prime
C क्योंकि 3465 को तोड़ा नहीं जा सकता / Because 3465 cannot be factorised
D क्योंकि गुणनफल बदल जाता है / Because the product changes
Explanation opens after your attempt
Correct Answer
A. क्योंकि 8 और 3465 संयुक्त रूप हैं / Because 8 and 3465 are composite forms
Step 1
Concept
अभाज्य गुणनखंडन में हर अंतिम गुणनखंड अभाज्य आधार में होना चाहिए। / In prime factorisation, every final factor should be in prime-base form.
Step 2
Why this answer is correct
\(8=2^3\) और \(3465=3^2\times5\times7\times11\) है। / \(8=2^3\) and \(3465=3^2\times5\times7\times11\).
Step 3
Exam Tip
इसलिए अंतिम रूप \(2^3\times3^2\times5\times7\times11\) होगा। / Therefore, the final form is \(2^3\times3^2\times5\times7\times11\).
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अंतिम अभाज्य गुणनखंडन में संयुक्त आधार को क्यों हटाना जरूरी होता है?
Why is it necessary to remove a composite base in the final prime factorisation?
#prime-factorisation
#final-form
#hard
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A क्योंकि अंतिम रूप में केवल अभाज्य आधार होने चाहिए / Because only prime bases should remain in the final form
B क्योंकि संयुक्त आधार से संख्या हमेशा बदल जाती है / Because a composite base always changes the number
C क्योंकि घातों का उपयोग नहीं किया जा सकता / Because powers cannot be used
D क्योंकि हर संख्या को केवल दो गुणनखंडों में लिखना होता है / Because every number must be written in only two factors
Explanation opens after your attempt
Correct Answer
A. क्योंकि अंतिम रूप में केवल अभाज्य आधार होने चाहिए / Because only prime bases should remain in the final form
Step 1
Concept
अभाज्य गुणनखंडन का अंतिम रूप केवल अभाज्य संख्याओं पर आधारित होता है। / The final form of prime factorisation is based only on prime numbers.
Step 2
Why this answer is correct
यदि (45) जैसा आधार बचा है, तो \(45=3^2\times5\) लिखना होगा। / If a base like (45) remains, it must be written as \(45=3^2\times5\).
Step 3
Exam Tip
परीक्षा में अंतिम उत्तर लिखने से पहले हर आधार की जांच करें। / In exams, check every base before writing the final answer.
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संख्या 14256 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 14256?
#prime-factorisation
#number-14256
#hard
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A \(2^4\times3^4\times11\)
B \(2^3\times3^4\times11\)
C \(16\times891\)
D \(2^4\times81\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^4\times11\)
Step 1
Concept
\(14256=16\times891\) लिखें। / Write \(14256=16\times891\).
Step 2
Why this answer is correct
\(16=2^4\) और \(891=3^4\times11\), इसलिए \(14256=2^4\times3^4\times11\)। / \(16=2^4\) and \(891=3^4\times11\), so \(14256=2^4\times3^4\times11\).
Step 3
Exam Tip
891 को अंतिम रूप में न छोड़ें। / Do not leave 891 in the final form.
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संख्या 18144 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 18144?
#prime-factorisation
#number-18144
#hard
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A \(2^5\times3^4\times7\)
B \(2^4\times3^4\times7\)
C \(32\times567\)
D \(2^5\times81\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^4\times7\)
Step 1
Concept
\(18144=32\times567\) लिखें। / Write \(18144=32\times567\).
Step 2
Why this answer is correct
\(32=2^5\) और \(567=3^4\times7\), इसलिए \(18144=2^5\times3^4\times7\)। / \(32=2^5\) and \(567=3^4\times7\), so \(18144=2^5\times3^4\times7\).
Step 3
Exam Tip
567 को पूरा अभाज्य रूप दें। / Give 567 its complete prime form.
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संख्या 24200 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 24200?
#prime-factorisation
#number-24200
#hard
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A \(2^3\times5^2\times11^2\)
B \(2^4\times5^2\times11\)
C \(200\times121\)
D \(8\times3025\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times5^2\times11^2\)
Step 1
Concept
\(24200=200\times121\) लिखें। / Write \(24200=200\times121\).
Step 2
Why this answer is correct
\(200=2^3\times5^2\) और \(121=11^2\), इसलिए \(24200=2^3\times5^2\times11^2\)। / \(200=2^3\times5^2\) and \(121=11^2\), so \(24200=2^3\times5^2\times11^2\).
Step 3
Exam Tip
200 और 121 को अंतिम रूप में न छोड़ें। / Do not leave 200 and 121 in the final form.
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संख्या 25410 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 25410?
#prime-factorisation
#number-25410
#hard
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A \(2\times3\times5\times7\times11^2\)
B \(2^2\times3\times5\times7\times11\)
C \(210\times121\)
D \(2\times105\times121\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\times7\times11^2\)
Step 1
Concept
\(25410=210\times121\) लिखें। / Write \(25410=210\times121\).
Step 2
Why this answer is correct
\(210=2\times3\times5\times7\) और \(121=11^2\), इसलिए \(25410=2\times3\times5\times7\times11^2\)। / \(210=2\times3\times5\times7\) and \(121=11^2\), so \(25410=2\times3\times5\times7\times11^2\).
Step 3
Exam Tip
210 और 121 दोनों को अभाज्य रूप दें। / Give prime form to both 210 and 121.
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संख्या 27216 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 27216?
#prime-factorisation
#number-27216
#hard
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A \(2^4\times3^5\times7\)
B \(2^3\times3^5\times7\)
C \(16\times1701\)
D \(2^4\times243\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^5\times7\)
Step 1
Concept
\(27216=16\times1701\) लिखें। / Write \(27216=16\times1701\).
Step 2
Why this answer is correct
\(1701=3^5\times7\), इसलिए \(27216=2^4\times3^5\times7\)। / \(1701=3^5\times7\), so \(27216=2^4\times3^5\times7\).
Step 3
Exam Tip
1701 को 3 और 7 के अभाज्य रूप में बदलें। / Convert 1701 into prime form using 3 and 7.
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संख्या 30240 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 30240?
#prime-factorisation
#number-30240
#hard
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A \(2^5\times3^3\times5\times7\)
B \(2^4\times3^3\times5\times7\)
C \(32\times945\)
D \(2^5\times27\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^3\times5\times7\)
Step 1
Concept
\(30240=32\times945\) लिखें। / Write \(30240=32\times945\).
Step 2
Why this answer is correct
\(945=3^3\times5\times7\), इसलिए \(30240=2^5\times3^3\times5\times7\)। / \(945=3^3\times5\times7\), so \(30240=2^5\times3^3\times5\times7\).
Step 3
Exam Tip
945 को अंतिम उत्तर में न रखें। / Do not keep 945 in the final answer.
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संख्या 36300 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 36300?
#prime-factorisation
#number-36300
#hard
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A \(2^2\times3\times5^2\times11^2\)
B \(2\times3^2\times5^2\times11\)
C \(300\times121\)
D \(4\times9075\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times5^2\times11^2\)
Step 1
Concept
\(36300=300\times121\) लिखें। / Write \(36300=300\times121\).
Step 2
Why this answer is correct
\(300=2^2\times3\times5^2\) और \(121=11^2\), इसलिए \(36300=2^2\times3\times5^2\times11^2\)। / \(300=2^2\times3\times5^2\) and \(121=11^2\), so \(36300=2^2\times3\times5^2\times11^2\).
Step 3
Exam Tip
300 और 121 को अभाज्य घातों में बदलें। / Convert 300 and 121 into prime powers.
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संख्या 38115 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 38115?
#prime-factorisation
#number-38115
#hard
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A \(3^2\times5\times7\times11^2\)
B \(3^3\times5\times7\times11\)
C \(315\times121\)
D \(9\times4235\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5\times7\times11^2\)
Step 1
Concept
\(38115=315\times121\) लिखें। / Write \(38115=315\times121\).
Step 2
Why this answer is correct
\(315=3^2\times5\times7\) और \(121=11^2\), इसलिए \(38115=3^2\times5\times7\times11^2\)। / \(315=3^2\times5\times7\) and \(121=11^2\), so \(38115=3^2\times5\times7\times11^2\).
Step 3
Exam Tip
दोनों भागों को पूरा तोड़ें। / Break both parts completely.
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संख्या 43200 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 43200?
#prime-factorisation
#number-43200
#hard
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A \(2^6\times3^3\times5^2\)
B \(2^5\times3^3\times5^2\)
C \(432\times100\)
D \(64\times675\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^3\times5^2\)
Step 1
Concept
\(43200=432\times100\) लिखें। / Write \(43200=432\times100\).
Step 2
Why this answer is correct
\(432=2^4\times3^3\) और \(100=2^2\times5^2\), इसलिए \(43200=2^6\times3^3\times5^2\)। / \(432=2^4\times3^3\) and \(100=2^2\times5^2\), so \(43200=2^6\times3^3\times5^2\).
Step 3
Exam Tip
2 की कुल घात 6 गिनें। / Count the total power of 2 as 6.
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संख्या 48510 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 48510?
#prime-factorisation
#number-48510
#hard
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A \(2\times3^2\times5\times7^2\times11\)
B \(2^2\times3\times5\times7^2\times11\)
C \(90\times539\)
D \(2\times45\times539\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\times7^2\times11\)
Step 1
Concept
\(48510=90\times539\) लिखें। / Write \(48510=90\times539\).
Step 2
Why this answer is correct
\(90=2\times3^2\times5\) और \(539=7^2\times11\), इसलिए \(48510=2\times3^2\times5\times7^2\times11\)। / \(90=2\times3^2\times5\) and \(539=7^2\times11\), so \(48510=2\times3^2\times5\times7^2\times11\).
Step 3
Exam Tip
90 और 539 दोनों को अभाज्य रूप दें। / Give prime form to both 90 and 539.
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संख्या 52920 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 52920?
#prime-factorisation
#number-52920
#hard
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? Hint Small clue
A \(2^3\times3^3\times5\times7^2\)
B \(2^4\times3^2\times5\times7^2\)
C \(8\times6615\)
D \(2^3\times135\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times5\times7^2\)
Step 1
Concept
\(52920=8\times6615\) लिखें। / Write \(52920=8\times6615\).
Step 2
Why this answer is correct
\(6615=3^3\times5\times7^2\), इसलिए \(52920=2^3\times3^3\times5\times7^2\)। / \(6615=3^3\times5\times7^2\), so \(52920=2^3\times3^3\times5\times7^2\).
Step 3
Exam Tip
6615 को पूरा अभाज्य रूप दें। / Give 6615 its complete prime form.
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संख्या 59290 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 59290?
#prime-factorisation
#number-59290
#hard
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A \(2\times5\times7\times11^3\)
B \(2^2\times5\times7\times11^2\)
C \(70\times1331\)
D \(10\times5929\)
Explanation opens after your attempt
Correct Answer
A. \(2\times5\times7\times11^3\)
Step 1
Concept
\(59290=70\times1331\) लिखें। / Write \(59290=70\times1331\).
Step 2
Why this answer is correct
\(70=2\times5\times7\) और \(1331=11^3\), इसलिए \(59290=2\times5\times7\times11^3\)। / \(70=2\times5\times7\) and \(1331=11^3\), so \(59290=2\times5\times7\times11^3\).
Step 3
Exam Tip
1331 को \(11^3\) में बदलें। / Change 1331 into \(11^3\).
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संख्या 65536 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 65536?
#prime-factorisation
#power-of-two
#hard
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? Hint Small clue
A \(2^{16}\)
B \(2^{15}\)
C \(256^2\)
D \(16^4\)
Explanation opens after your attempt
Correct Answer
A. \(2^{16}\)
Step 1
Concept
65536 को 2 से बार-बार भाग दें। / Divide 65536 repeatedly by 2.
Step 2
Why this answer is correct
सोलह बार 2 मिलने से \(65536=2^{16}\) होता है। / Sixteen factors of 2 give \(65536=2^{16}\).
Step 3
Exam Tip
256 और 16 संयुक्त आधार हैं, इसलिए अंतिम रूप में 2 की घात लिखें। / 256 and 16 are composite bases, so write the power of 2 in final form.
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संख्या 68040 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 68040?
#prime-factorisation
#number-68040
#hard
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? Hint Small clue
A \(2^3\times3^5\times5\times7\)
B \(2^2\times3^5\times5\times7\)
C \(8\times8505\)
D \(2^3\times243\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^5\times5\times7\)
Step 1
Concept
\(68040=8\times8505\) लिखें। / Write \(68040=8\times8505\).
Step 2
Why this answer is correct
\(8505=3^5\times5\times7\), इसलिए \(68040=2^3\times3^5\times5\times7\)। / \(8505=3^5\times5\times7\), so \(68040=2^3\times3^5\times5\times7\).
Step 3
Exam Tip
8505 को अभाज्य घातों में बदलें। / Convert 8505 into prime powers.
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संख्या 76230 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 76230?
#prime-factorisation
#number-76230
#hard
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? Hint Small clue
A \(2\times3^2\times5\times7\times11^2\)
B \(2^2\times3\times5\times7\times11^2\)
C \(630\times121\)
D \(2\times315\times121\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\times7\times11^2\)
Step 1
Concept
\(76230=630\times121\) लिखें। / Write \(76230=630\times121\).
Step 2
Why this answer is correct
\(630=2\times3^2\times5\times7\) और \(121=11^2\), इसलिए \(76230=2\times3^2\times5\times7\times11^2\)। / \(630=2\times3^2\times5\times7\) and \(121=11^2\), so \(76230=2\times3^2\times5\times7\times11^2\).
Step 3
Exam Tip
630 और 121 दोनों को पूरा तोड़ें। / Break both 630 and 121 completely.
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संख्या 88200 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 88200?
#prime-factorisation
#number-88200
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^3\times3^2\times5^2\times7^2\)
B \(2^2\times3^2\times5^2\times7^2\)
C \(8\times11025\)
D \(2^3\times105^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5^2\times7^2\)
Step 1
Concept
\(88200=8\times11025\) लिखें। / Write \(88200=8\times11025\).
Step 2
Why this answer is correct
\(11025=3^2\times5^2\times7^2\), इसलिए \(88200=2^3\times3^2\times5^2\times7^2\)। / \(11025=3^2\times5^2\times7^2\), so \(88200=2^3\times3^2\times5^2\times7^2\).
Step 3
Exam Tip
11025 को अभाज्य घातों में बदलें। / Convert 11025 into prime powers.
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संख्या 95256 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 95256?
#prime-factorisation
#number-95256
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^3\times3^5\times7^2\)
B \(2^4\times3^4\times7^2\)
C \(8\times11907\)
D \(2^3\times243\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^5\times7^2\)
Step 1
Concept
\(95256=8\times11907\) लिखें। / Write \(95256=8\times11907\).
Step 2
Why this answer is correct
\(11907=3^5\times7^2\), इसलिए \(95256=2^3\times3^5\times7^2\)। / \(11907=3^5\times7^2\), so \(95256=2^3\times3^5\times7^2\).
Step 3
Exam Tip
11907 को 3 और 7 की घातों में बदलें। / Convert 11907 into powers of 3 and 7.
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संख्या 108900 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 108900?
#prime-factorisation
#square-number
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^2\times3^2\times5^2\times11^2\)
B \(2\times3^2\times5^2\times11^2\)
C \(900\times121\)
D \(4\times27225\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times5^2\times11^2\)
Step 1
Concept
\(108900=900\times121\) लिखें। / Write \(108900=900\times121\).
Step 2
Why this answer is correct
\(900=2^2\times3^2\times5^2\) और \(121=11^2\), इसलिए \(108900=2^2\times3^2\times5^2\times11^2\)। / \(900=2^2\times3^2\times5^2\) and \(121=11^2\), so \(108900=2^2\times3^2\times5^2\times11^2\).
Step 3
Exam Tip
यह वर्ग रूप है, इसलिए सभी घातें सम हैं। / This is a square form, so all exponents are even.
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संख्या 127008 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 127008?
#prime-factorisation
#number-127008
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^5\times3^4\times7^2\)
B \(2^4\times3^5\times7^2\)
C \(32\times3969\)
D \(2^5\times81\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^4\times7^2\)
Step 1
Concept
\(127008=32\times3969\) लिखें। / Write \(127008=32\times3969\).
Step 2
Why this answer is correct
\(3969=3^4\times7^2\), इसलिए \(127008=2^5\times3^4\times7^2\)। / \(3969=3^4\times7^2\), so \(127008=2^5\times3^4\times7^2\).
Step 3
Exam Tip
3969 को अभाज्य घातों में बदलें। / Convert 3969 into prime powers.
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संख्या 130680 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 130680?
#prime-factorisation
#number-130680
#hard
50 50-50 2 wrong hide
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A \(2^3\times3^3\times5\times11^2\)
B \(2^2\times3^4\times5\times11^2\)
C \(1080\times121\)
D \(8\times16335\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times5\times11^2\)
Step 1
Concept
\(130680=1080\times121\) लिखें। / Write \(130680=1080\times121\).
Step 2
Why this answer is correct
\(1080=2^3\times3^3\times5\) और \(121=11^2\), इसलिए \(130680=2^3\times3^3\times5\times11^2\)। / \(1080=2^3\times3^3\times5\) and \(121=11^2\), so \(130680=2^3\times3^3\times5\times11^2\).
Step 3
Exam Tip
1080 और 121 को पूरा तोड़ें। / Break 1080 and 121 completely.
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यदि \(127008=2^a\times3^4\times7^2\), तो (a) का मान क्या है?
If \(127008=2^a\times3^4\times7^2\), what is the value of (a)?
#exponent-comparison
#number-127008
#hard
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? Hint Small clue
A 5
B 4
C 6
D 7
Explanation opens after your attempt
Step 1
Concept
\(127008=32\times3969\) है। / \(127008=32\times3969\).
Step 2
Why this answer is correct
\(32=2^5\) और \(3969=3^4\times7^2\), इसलिए 2 की घात 5 है। / \(32=2^5\) and \(3969=3^4\times7^2\), so the power of 2 is 5.
Step 3
Exam Tip
तुलना करने पर (a=5) मिलता है। / Comparing gives (a=5).
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यदि \(95256=2^3\times3^b\times7^2\), तो (b) का मान क्या है?
If \(95256=2^3\times3^b\times7^2\), what is the value of (b)?
#exponent-comparison
#number-95256
#hard
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A 5
B 4
C 6
D 3
Explanation opens after your attempt
Step 1
Concept
\(95256=8\times11907\) लिखें। / Write \(95256=8\times11907\).
Step 2
Why this answer is correct
\(11907=3^5\times7^2\), इसलिए \(95256=2^3\times3^5\times7^2\)। / \(11907=3^5\times7^2\), so \(95256=2^3\times3^5\times7^2\).
Step 3
Exam Tip
दिए गए रूप से (b=5) है। / From the given form, (b=5).
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यदि \(108900=2^2\times3^2\times5^m\times11^2\), तो (m) का मान क्या है?
If \(108900=2^2\times3^2\times5^m\times11^2\), what is the value of (m)?
#exponent-comparison
#square-number
#hard
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A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
\(108900=900\times121\) है। / \(108900=900\times121\).
Step 2
Why this answer is correct
\(900=2^2\times3^2\times5^2\) और \(121=11^2\), इसलिए 5 की घात 2 है। / \(900=2^2\times3^2\times5^2\) and \(121=11^2\), so the power of 5 is 2.
Step 3
Exam Tip
तुलना करने पर (m=2) होगा। / Comparing gives (m=2).
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यदि \(68040=2^3\times3^p\times5\times7\), तो (p) का मान क्या है?
If \(68040=2^3\times3^p\times5\times7\), what is the value of (p)?
#exponent-comparison
#number-68040
#hard
50 50-50 2 wrong hide
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? Hint Small clue
A 5
B 4
C 6
D 3
Explanation opens after your attempt
Step 1
Concept
\(68040=8\times8505\) लिखें। / Write \(68040=8\times8505\).
Step 2
Why this answer is correct
\(8505=3^5\times5\times7\), इसलिए 3 की घात 5 है। / \(8505=3^5\times5\times7\), so the power of 3 is 5.
Step 3
Exam Tip
तुलना करने पर (p=5) मिलेगा। / Comparing gives (p=5).
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किस संख्या का अभाज्य गुणनखंडन \(2^4\times3^4\times11\) है?
Which number has prime factorisation \(2^4\times3^4\times11\)?
#evaluate-factorisation
#number-14256
#hard
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A 14256
B 7128
C 28512
D 18144
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(3^4=81\) निकालें। / Calculate \(2^4=16\) and \(3^4=81\).
Step 2
Why this answer is correct
\(16\times81\times11=14256\)। / \(16\times81\times11=14256\).
Step 3
Exam Tip
घातों को पहले हल करें, फिर 11 से गुणा करें। / Solve powers first, then multiply by 11.
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किस संख्या का अभाज्य गुणनखंडन \(2^5\times3^4\times7\) है?
Which number has prime factorisation \(2^5\times3^4\times7\)?
#evaluate-factorisation
#number-18144
#hard
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A 18144
B 9072
C 36288
D 12096
Explanation opens after your attempt
Step 1
Concept
\(2^5=32\) और \(3^4=81\) निकालें। / Calculate \(2^5=32\) and \(3^4=81\).
Step 2
Why this answer is correct
\(32\times81\times7=18144\)। / \(32\times81\times7=18144\).
Step 3
Exam Tip
बड़ी घातों का मान पहले निकालना ठीक रहता है। / It is better to find higher powers first.
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किस संख्या का अभाज्य गुणनखंडन \(2\times3\times5\times7\times11^2\) है?
Which number has prime factorisation \(2\times3\times5\times7\times11^2\)?
#evaluate-factorisation
#number-25410
#hard
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A 25410
B 12705
C 50820
D 27720
Explanation opens after your attempt
Step 1
Concept
\(11^2=121\) निकालें। / Calculate \(11^2=121\).
Step 2
Why this answer is correct
\(2\times3\times5\times7\times121=25410\)। / \(2\times3\times5\times7\times121=25410\).
Step 3
Exam Tip
पहले छोटे गुणनखंडों का गुणनफल 210 लें, फिर 121 से गुणा करें। / First take the product of smaller factors as 210, then multiply by 121.
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किस संख्या का अभाज्य गुणनखंडन \(2^6\times3^3\times5^2\) है?
Which number has prime factorisation \(2^6\times3^3\times5^2\)?
#evaluate-factorisation
#number-43200
#hard
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A 43200
B 21600
C 86400
D 32400
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\), \(3^3=27\) और \(5^2=25\) निकालें। / Calculate \(2^6=64\), \(3^3=27\), and \(5^2=25\).
Step 2
Why this answer is correct
\(64\times27\times25=43200\)। / \(64\times27\times25=43200\).
Step 3
Exam Tip
तीनों घातों को अलग-अलग सरल करें। / Simplify all three powers separately.
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किस संख्या का अभाज्य गुणनखंडन \(2^5\times3^4\times7^2\) है?
Which number has prime factorisation \(2^5\times3^4\times7^2\)?
#evaluate-factorisation
#number-127008
#hard
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A 127008
B 63504
C 254016
D 95256
Explanation opens after your attempt
Step 1
Concept
\(2^5=32\), \(3^4=81\) और \(7^2=49\) निकालें। / Calculate \(2^5=32\), \(3^4=81\), and \(7^2=49\).
Step 2
Why this answer is correct
\(32\times81\times49=127008\)। / \(32\times81\times49=127008\).
Step 3
Exam Tip
घातों को पहले हल करने से गुणा साफ रहता है। / Solving powers first keeps multiplication clear.
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यदि संख्या \(2^8\times3^5\times5^2\times7^3\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^8\times3^5\times5^2\times7^3\), by which smallest number should it be multiplied to make a perfect square?
#perfect-square
#prime-exponents
#hard
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A 21
B 3
C 7
D 35
Explanation opens after your attempt
Step 1
Concept
पूर्ण वर्ग में सभी घातें सम होनी चाहिए। / In a perfect square, all exponents should be even.
Step 2
Why this answer is correct
3 की घात 5 और 7 की घात 3 विषम हैं। / The powers of 3 and 7 are odd.
Step 3
Exam Tip
\(3\times7=21\) से गुणा करने पर दोनों घातें सम हो जाएंगी। / Multiplying by \(3\times7=21\) makes both powers even.
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यदि संख्या \(2^9\times3^4\times5^7\times11^2\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^9\times3^4\times5^7\times11^2\), by which smallest number should it be divided to make a perfect square?
#perfect-square
#division
#hard
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A \(2\times5\)
B \(2^2\times5\)
C \(2\times5^2\)
D \(5\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2\times5\)
Step 1
Concept
पूर्ण वर्ग के लिए घातें सम चाहिए। / For a perfect square, exponents should be even.
Step 2
Why this answer is correct
2 की घात 9 और 5 की घात 7 विषम हैं। / The powers of 2 and 5 are odd.
Step 3
Exam Tip
\(2\times5\) से भाग देने पर घातें 8 और 6 हो जाएंगी। / Dividing by \(2\times5\) makes the powers 8 and 6.
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यदि संख्या \(2^5\times3^7\times5^4\times13^2\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^5\times3^7\times5^4\times13^2\), by which smallest number should it be multiplied to make a perfect cube?
#perfect-cube
#prime-exponents
#hard
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? Hint Small clue
A \(2\times3^2\times5^2\times13\)
B \(2\times3\times5\times13\)
C \(2^2\times3^2\times5\times13\)
D \(3^2\times5^2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5^2\times13\)
Step 1
Concept
पूर्ण घन में हर घात 3 का गुणज होनी चाहिए। / In a perfect cube, every exponent must be a multiple of 3.
Step 2
Why this answer is correct
5 को 6, 7 को 9, 4 को 6 और 2 को 3 बनाना होगा। / Powers 5, 7, 4, and 2 must become 6, 9, 6, and 3.
Step 3
Exam Tip
सबसे छोटा गुणक \(2\times3^2\times5^2\times13\) है। / The smallest multiplier is \(2\times3^2\times5^2\times13\).
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यदि संख्या \(2^{10}\times3^8\times5^5\times7^4\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^{10}\times3^8\times5^5\times7^4\), by which smallest number should it be divided to make a perfect cube?
#perfect-cube
#division
#hard
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? Hint Small clue
A \(2\times3^2\times5^2\times7\)
B \(2^2\times3\times5\times7\)
C \(2\times3\times5^2\times7^2\)
D \(3^2\times5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5^2\times7\)
Step 1
Concept
पूर्ण घन के लिए घातें 3 के गुणज चाहिए। / For a perfect cube, exponents should be multiples of 3.
Step 2
Why this answer is correct
10 को 9, 8 को 6, 5 को 3 और 4 को 3 तक घटाना सबसे छोटा तरीका है। / Reducing 10 to 9, 8 to 6, 5 to 3, and 4 to 3 is the smallest way.
Step 3
Exam Tip
इसलिए भाजक \(2\times3^2\times5^2\times7\) है। / Therefore, the divisor is \(2\times3^2\times5^2\times7\).
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यदि \(n=2^8\times3^6\times5^4\times11^2\), तो (n) किस संख्या से विभाज्य नहीं होगा?
If \(n=2^8\times3^6\times5^4\times11^2\), by which number will (n) not be divisible?
#divisibility
#prime-exponents
#hard
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? Hint Small clue
A \(11^3\)
B \(2^7\times3^5\)
C \(3^6\times5^3\)
D \(2^8\times11^2\)
Explanation opens after your attempt
Correct Answer
A. \(11^3\)
Step 1
Concept
भाजक की हर अभाज्य घात संख्या में उपलब्ध होनी चाहिए। / Every prime power of a divisor must be available in the number.
Step 2
Why this answer is correct
(n) में 11 की घात 2 है, पर \(11^3\) के लिए घात 3 चाहिए। / (n) has power 2 of 11, but \(11^3\) needs power 3.
Step 3
Exam Tip
इसलिए (n), \(11^3\) से विभाज्य नहीं होगा। / Therefore, (n) is not divisible by \(11^3\).
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यदि \(n=2^{10}\times3^5\times7^4\times13^2\), तो (n) किस संख्या से अवश्य विभाज्य होगा?
If \(n=2^{10}\times3^5\times7^4\times13^2\), by which number must (n) be divisible?
#divisibility
#prime-exponents
#hard
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? Hint Small clue
A \(2^9\times3^4\times7^3\times13\)
B \(2^{11}\times3^4\)
C \(3^6\times7^2\)
D \(2^{10}\times13^3\)
Explanation opens after your attempt
Correct Answer
A. \(2^9\times3^4\times7^3\times13\)
Step 1
Concept
विभाज्यता के लिए भाजक की घातें दी गई संख्या की घातों से अधिक नहीं होनी चाहिए। / For divisibility, exponents in the divisor must not exceed those in the given number.
Step 2
Why this answer is correct
\(2^9\), \(3^4\), \(7^3\) और 13 सभी (n) में उपलब्ध हैं। / \(2^9\), \(3^4\), \(7^3\), and 13 are all available in (n).
Step 3
Exam Tip
इसलिए (n) पहले विकल्प से अवश्य विभाज्य होगा। / Therefore, (n) must be divisible by the first option.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^9\times3^7\times5^4\times7^3\times11^2\) है, तो दोहराव सहित अभाज्य गुणनखंडों की संख्या कितनी है?
If a number has prime factorisation \(2^9\times3^7\times5^4\times7^3\times11^2\), how many prime factors does it have with repetition?
#counting-prime-factors
#prime-exponents
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 25
B 5
C 20
D 27
Explanation opens after your attempt
Step 1
Concept
दोहराव सहित गिनती में घातों को जोड़ा जाता है। / To count with repetition, add the exponents.
Step 2
Why this answer is correct
(9+7+4+3+2=25)। / (9+7+4+3+2=25).
Step 3
Exam Tip
आधारों की संख्या और दोहराव सहित कुल संख्या को अलग रखें। / Keep the number of bases and the total count with repetition separate.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^6\times3^5\times7^4\times11^3\times13^2\) है, तो उसमें अलग-अलग अभाज्य गुणनखंड कितने हैं?
If a number has prime factorisation \(2^6\times3^5\times7^4\times11^3\times13^2\), how many distinct prime factors does it have?
#distinct-prime-factors
#prime-exponents
#hard
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 5
B 20
C 6
D 4
Explanation opens after your attempt
Step 1
Concept
अलग-अलग अभाज्य गिनते समय केवल आधार गिने जाते हैं। / While counting distinct primes, only bases are counted.
Step 2
Why this answer is correct
आधार 2, 3, 7, 11 और 13 हैं। / The bases are 2, 3, 7, 11, and 13.
Step 3
Exam Tip
इसलिए अलग-अलग अभाज्य गुणनखंडों की संख्या 5 है। / Therefore, the number of distinct prime factors is 5.
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यदि \(a=2^6\times3^4\times5^2\times11\) और \(b=2^3\times3^5\times7\times11^2\), तो (ab) में 3 की घात क्या होगी?
If \(a=2^6\times3^4\times5^2\times11\) and \(b=2^3\times3^5\times7\times11^2\), what will be the power of 3 in (ab)?
#product-factorisation
#powers
#hard
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+10 Time+ 10 sec extra
? Hint Small clue
A 9
B 5
C 4
D 8
Explanation opens after your attempt
Step 1
Concept
गुणा में समान अभाज्य आधार की घातें जुड़ती हैं। / In multiplication, powers of the same prime base are added.
Step 2
Why this answer is correct
(a) में 3 की घात 4 है और (b) में 3 की घात 5 है। / The power of 3 in (a) is 4 and in (b) is 5.
Step 3
Exam Tip
(ab) में 3 की घात (4+5=9) होगी। / In (ab), the power of 3 will be (4+5=9).
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यदि \(x=2^8\times5^3\times7^2\times13\) और \(y=2^5\times3^2\times5^4\times13^3\), तो (xy) में 13 की घात क्या होगी?
If \(x=2^8\times5^3\times7^2\times13\) and \(y=2^5\times3^2\times5^4\times13^3\), what will be the power of 13 in (xy)?
#product-factorisation
#powers
#hard
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A 4
B 3
C 1
D 5
Explanation opens after your attempt
Step 1
Concept
समान आधार 13 की घातें गुणा में जुड़ेंगी। / Powers with the same base 13 are added in multiplication.
Step 2
Why this answer is correct
(x) में 13 की घात 1 है और (y) में 13 की घात 3 है। / The power of 13 in (x) is 1 and in (y) is 3.
Step 3
Exam Tip
कुल घात (1+3=4) होगी। / The total power will be (1+3=4).
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किस विकल्प में \(2^5\times3^4\times7^2\) का सही मान है?
Which option gives the correct value of \(2^5\times3^4\times7^2\)?
#evaluate-factorisation
#number-127008
#hard
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A 127008
B 63504
C 254016
D 95256
Explanation opens after your attempt
Step 1
Concept
\(2^5=32\), \(3^4=81\) और \(7^2=49\) निकालें। / Calculate \(2^5=32\), \(3^4=81\), and \(7^2=49\).
Step 2
Why this answer is correct
\(32\times81\times49=127008\)। / \(32\times81\times49=127008\).
Step 3
Exam Tip
तीनों घातों को पहले अलग-अलग हल करें। / Solve all three powers separately first.
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किस विकल्प में \(2^3\times3^5\times7^2\) का सही मान है?
Which option gives the correct value of \(2^3\times3^5\times7^2\)?
#evaluate-factorisation
#number-95256
#hard
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A 95256
B 47628
C 190512
D 68040
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\), \(3^5=243\) और \(7^2=49\) निकालें। / Calculate \(2^3=8\), \(3^5=243\), and \(7^2=49\).
Step 2
Why this answer is correct
\(8\times243\times49=95256\)। / \(8\times243\times49=95256\).
Step 3
Exam Tip
बड़ी घातों को पहले सरल करें। / Simplify higher powers first.
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किस विकल्प में केवल अंतिम अभाज्य गुणनखंडन दिया गया है?
Which option gives only the final prime factorisation?
#prime-factorisation
#final-form
#hard
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A \(2^3\times3^3\times5\times7^2\)
B \(8\times135\times49\)
C \(2^3\times27\times245\)
D \(216\times245\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times5\times7^2\)
Step 1
Concept
अंतिम रूप में हर आधार अभाज्य होना चाहिए। / In the final form, every base must be prime.
Step 2
Why this answer is correct
पहले विकल्प में आधार 2, 3, 5 और 7 अभाज्य हैं। / In the first option, bases 2, 3, 5, and 7 are prime.
Step 3
Exam Tip
8, 135, 49, 27, 245 और 216 संयुक्त हैं, इसलिए वे अंतिम रूप नहीं हैं। / 8, 135, 49, 27, 245, and 216 are composite, so they are not final forms.
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किस विकल्प में अभाज्य गुणनखंडन अधूरा है?
Which option has incomplete prime factorisation?
#prime-factorisation
#incomplete-form
#hard
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A \(2^5\times81\times49\)
B \(2^5\times3^4\times7^2\)
C \(2^6\times3^3\times5^2\)
D \(2\times5\times7\times11^3\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times81\times49\)
Step 1
Concept
अधूरे रूप में संयुक्त आधार बच जाता है। / In an incomplete form, composite bases remain.
Step 2
Why this answer is correct
81 और 49 संयुक्त आधार हैं। / 81 and 49 are composite bases.
Step 3
Exam Tip
\(2^5\times81\times49\) को \(2^5\times3^4\times7^2\) में बदलना होगा। / \(2^5\times81\times49\) must be changed into \(2^5\times3^4\times7^2\).
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यदि \(2^6\times3^3\times5^2\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^6\times3^3\times5^2\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#hard
#mcq
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A 43200
B 21600
C 86400
D 32400
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\), \(3^3=27\) और \(5^2=25\) हैं। / \(2^6=64\), \(3^3=27\), and \(5^2=25\).
Step 2
Why this answer is correct
\(64\times27\times25=43200\)। / \(64\times27\times25=43200\).
Step 3
Exam Tip
घातों को पहले हल करने से सही विकल्प जल्दी मिलता है। / Solving powers first helps find the correct option quickly.
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यदि \(2^2\times3^2\times5^2\times11^2\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^2\times3^2\times5^2\times11^2\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#square-number
#hard
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A 108900
B 54450
C 217800
D 27225
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\), \(3^2=9\), \(5^2=25\) और \(11^2=121\) निकालें। / Calculate \(2^2=4\), \(3^2=9\), \(5^2=25\), and \(11^2=121\).
Step 2
Why this answer is correct
\(4\times9\times25\times121=108900\)। / \(4\times9\times25\times121=108900\).
Step 3
Exam Tip
यह वर्ग रूप है, इसलिए घातों को ध्यान से देखें। / This is a square form, so observe the powers carefully.
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संख्या 158760 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 158760?
#prime-factorisation
#number-158760
#hard
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A \(2^3\times3^4\times5\times7^2\)
B \(2^4\times3^3\times5\times7^2\)
C \(8\times19845\)
D \(2^3\times405\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^4\times5\times7^2\)
Step 1
Concept
\(158760=8\times19845\) लिखें। / Write \(158760=8\times19845\).
Step 2
Why this answer is correct
\(19845=3^4\times5\times7^2\), इसलिए \(158760=2^3\times3^4\times5\times7^2\)। / \(19845=3^4\times5\times7^2\), so \(158760=2^3\times3^4\times5\times7^2\).
Step 3
Exam Tip
19845 को पूरी तरह तोड़ें। / Break 19845 completely.
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संख्या 217800 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 217800?
#prime-factorisation
#number-217800
#hard
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A \(2^3\times3^2\times5^2\times11^2\)
B \(2^2\times3^3\times5^2\times11^2\)
C \(8\times27225\)
D \(2^3\times225\times121\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5^2\times11^2\)
Step 1
Concept
\(217800=8\times27225\) लिखें। / Write \(217800=8\times27225\).
Step 2
Why this answer is correct
\(27225=3^2\times5^2\times11^2\), इसलिए \(217800=2^3\times3^2\times5^2\times11^2\)। / \(27225=3^2\times5^2\times11^2\), so \(217800=2^3\times3^2\times5^2\times11^2\).
Step 3
Exam Tip
27225 को अभाज्य घातों में बदलें। / Convert 27225 into prime powers.
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संख्या 279936 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 279936?
#prime-factorisation
#number-279936
#hard
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A \(2^7\times3^7\)
B \(2^6\times3^7\)
C \(128\times2187\)
D \(6^7\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^7\)
Step 1
Concept
\(279936=128\times2187\) लिखा जा सकता है। / (279936) can be written as \(128\times2187\).
Step 2
Why this answer is correct
\(128=2^7\) और \(2187=3^7\), इसलिए \(279936=2^7\times3^7\)। / \(128=2^7\) and \(2187=3^7\), so \(279936=2^7\times3^7\).
Step 3
Exam Tip
128 और 2187 को अंतिम रूप में न छोड़ें। / Do not leave 128 and 2187 in the final form.
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अभाज्य गुणनखंडन में \(8\times27225\) को अंतिम उत्तर क्यों नहीं माना जाएगा?
Why will \(8\times27225\) not be considered the final answer in prime factorisation?
#prime-factorisation
#concept-check
#hard
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A क्योंकि 8 और 27225 संयुक्त रूप हैं / Because 8 and 27225 are composite forms
B क्योंकि 8 अभाज्य संख्या है / Because 8 is prime
C क्योंकि 27225 को तोड़ा नहीं जा सकता / Because 27225 cannot be factorised
D क्योंकि गुणनफल बदल जाएगा / Because the product will change
Explanation opens after your attempt
Correct Answer
A. क्योंकि 8 और 27225 संयुक्त रूप हैं / Because 8 and 27225 are composite forms
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में हर आधार अभाज्य होना चाहिए। / In final prime factorisation, every base should be prime.
Step 2
Why this answer is correct
\(8=2^3\) और \(27225=3^2\times5^2\times11^2\) है। / \(8=2^3\) and \(27225=3^2\times5^2\times11^2\).
Step 3
Exam Tip
इसलिए अंतिम रूप \(2^3\times3^2\times5^2\times11^2\) होगा। / Therefore, the final form is \(2^3\times3^2\times5^2\times11^2\).
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