संख्या 132 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 132?
#prime-factorisation
#number-132
#easy
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A \(2^2\times3\times11\)
B \(4\times33\)
C \(2\times66\)
D \(12\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times11\)
Step 1
Concept
\(132=4\times33\) लिखें। / Write \(132=4\times33\).
Step 2
Why this answer is correct
\(4=2^2\) और \(33=3\times11\), इसलिए \(132=2^2\times3\times11\)। / \(4=2^2\) and \(33=3\times11\), so \(132=2^2\times3\times11\).
Step 3
Exam Tip
अंतिम उत्तर में 4 और 33 जैसे संयुक्त गुणनखंड न रखें। / Do not keep composite factors like 4 and 33 in the final answer.
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संख्या 150 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 150?
#prime-factorisation
#number-150
#easy
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A \(2\times3\times5^2\)
B \(15\times10\)
C \(2\times75\)
D \(3^2\times5^2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5^2\)
Step 1
Concept
\(150=15\times10\) लिखें। / Write \(150=15\times10\).
Step 2
Why this answer is correct
\(15=3\times5\) और \(10=2\times5\), इसलिए \(150=2\times3\times5^2\)। / \(15=3\times5\) and \(10=2\times5\), so \(150=2\times3\times5^2\).
Step 3
Exam Tip
समान अभाज्य दो बार आए तो घात लिखें। / When the same prime repeats, write it as a power.
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संख्या 162 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 162?
#prime-factorisation
#number-162
#easy
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A \(2\times3^4\)
B \(2^2\times3^3\)
C \(18\times9\)
D \(6\times27\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^4\)
Step 1
Concept
\(162=2\times81\) लिखें। / Write \(162=2\times81\).
Step 2
Why this answer is correct
\(81=3^4\), इसलिए \(162=2\times3^4\)। / Since \(81=3^4\), \(162=2\times3^4\).
Step 3
Exam Tip
81 को अंतिम रूप में न छोड़कर \(3^4\) लिखें। / Do not leave 81 in the final form; write \(3^4\).
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संख्या 168 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 168?
#prime-factorisation
#number-168
#easy
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A \(2^3\times3\times7\)
B \(8\times21\)
C \(2^2\times42\)
D \(6\times28\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times7\)
Step 1
Concept
\(168=8\times21\) लिखें। / Write \(168=8\times21\).
Step 2
Why this answer is correct
\(8=2^3\) और \(21=3\times7\), इसलिए \(168=2^3\times3\times7\)। / \(8=2^3\) and \(21=3\times7\), so \(168=2^3\times3\times7\).
Step 3
Exam Tip
8 और 21 संयुक्त हैं, इसलिए उन्हें आगे तोड़ें। / 8 and 21 are composite, so break them further.
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संख्या 180 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 180?
#prime-factorisation
#number-180
#easy
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A \(2^2\times3^2\times5\)
B \(18\times10\)
C \(2\times90\)
D \(3^2\times20\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times5\)
Step 1
Concept
\(180=18\times10\) लिखें। / Write \(180=18\times10\).
Step 2
Why this answer is correct
\(18=2\times3^2\) और \(10=2\times5\), इसलिए \(180=2^2\times3^2\times5\)। / \(18=2\times3^2\) and \(10=2\times5\), so \(180=2^2\times3^2\times5\).
Step 3
Exam Tip
सभी संयुक्त गुणनखंडों को अभाज्य रूप में बदलें। / Change all composite factors into prime form.
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संख्या 196 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 196?
#prime-factorisation
#square-number
#easy
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A \(2^2\times7^2\)
B \(14\times14\)
C \(4\times49\)
D \(2\times98\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times7^2\)
Step 1
Concept
\(196=14\times14\) या \(4\times49\) लिखा जा सकता है। / (196) can be written as \(14\times14\) or \(4\times49\).
Step 2
Why this answer is correct
\(14=2\times7\), इसलिए \(196=2^2\times7^2\)। / Since \(14=2\times7\), \(196=2^2\times7^2\).
Step 3
Exam Tip
वर्ग संख्या में घातें अक्सर सम होती हैं, इसे जांचें। / In square numbers, exponents are often even, so check them.
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संख्या 210 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 210?
#prime-factorisation
#number-210
#easy
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A \(2\times3\times5\times7\)
B \(21\times10\)
C \(30\times7\)
D \(14\times15\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\times7\)
Step 1
Concept
\(210=21\times10\) लिखें। / Write \(210=21\times10\).
Step 2
Why this answer is correct
\(21=3\times7\) और \(10=2\times5\), इसलिए \(210=2\times3\times5\times7\)। / \(21=3\times7\) and \(10=2\times5\), so \(210=2\times3\times5\times7\).
Step 3
Exam Tip
अंतिम उत्तर में 21 या 10 न रखें। / Do not keep 21 or 10 in the final answer.
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संख्या 225 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 225?
#prime-factorisation
#square-number
#easy
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A \(3^2\times5^2\)
B \(15\times15\)
C \(9\times25\)
D \(3\times75\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5^2\)
Step 1
Concept
\(225=15^2\) पहचाना जा सकता है। / Recognise \(225=15^2\).
Step 2
Why this answer is correct
\(15=3\times5\), इसलिए \(225=3^2\times5^2\)। / Since \(15=3\times5\), \(225=3^2\times5^2\).
Step 3
Exam Tip
15 संयुक्त है, इसलिए अंतिम रूप में 3 और 5 की घातें लिखें। / 15 is composite, so write powers of 3 and 5 in the final form.
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संख्या 231 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 231?
#prime-factorisation
#number-231
#easy
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? Hint Small clue
A \(3\times7\times11\)
B \(21\times11\)
C \(33\times7\)
D \(3\times77\)
Explanation opens after your attempt
Correct Answer
A. \(3\times7\times11\)
Step 1
Concept
\(231=21\times11\) लिखें। / Write \(231=21\times11\).
Step 2
Why this answer is correct
\(21=3\times7\), इसलिए \(231=3\times7\times11\)। / Since \(21=3\times7\), \(231=3\times7\times11\).
Step 3
Exam Tip
21 संयुक्त है, इसलिए उसे अंतिम उत्तर में न रखें। / 21 is composite, so do not keep it in the final answer.
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संख्या 240 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 240?
#prime-factorisation
#number-240
#easy
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A \(2^4\times3\times5\)
B \(24\times10\)
C \(2^3\times30\)
D \(16\times15\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3\times5\)
Step 1
Concept
\(240=16\times15\) लिखें। / Write \(240=16\times15\).
Step 2
Why this answer is correct
\(16=2^4\) और \(15=3\times5\), इसलिए \(240=2^4\times3\times5\)। / \(16=2^4\) and \(15=3\times5\), so \(240=2^4\times3\times5\).
Step 3
Exam Tip
16 को \(2^4\) में बदलना जरूरी है। / It is necessary to change 16 into \(2^4\).
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संख्या 252 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 252?
#prime-factorisation
#number-252
#easy
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A \(2^2\times3^2\times7\)
B \(4\times63\)
C \(2\times126\)
D \(9\times28\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times7\)
Step 1
Concept
\(252=4\times63\) लिखें। / Write \(252=4\times63\).
Step 2
Why this answer is correct
\(4=2^2\) और \(63=3^2\times7\), इसलिए \(252=2^2\times3^2\times7\)। / \(4=2^2\) and \(63=3^2\times7\), so \(252=2^2\times3^2\times7\).
Step 3
Exam Tip
63 को भी पूरी तरह अभाज्य रूप में तोड़ें। / Break 63 completely into prime form too.
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संख्या 270 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 270?
#prime-factorisation
#number-270
#easy
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A \(2\times3^3\times5\)
B \(27\times10\)
C \(2^2\times3^2\times5\)
D \(9\times30\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^3\times5\)
Step 1
Concept
\(270=27\times10\) लिखें। / Write \(270=27\times10\).
Step 2
Why this answer is correct
\(27=3^3\) और \(10=2\times5\), इसलिए \(270=2\times3^3\times5\)। / \(27=3^3\) and \(10=2\times5\), so \(270=2\times3^3\times5\).
Step 3
Exam Tip
27 को \(3^3\) में बदलना न भूलें। / Do not forget to change 27 into \(3^3\).
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संख्या 294 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 294?
#prime-factorisation
#number-294
#easy
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A \(2\times3\times7^2\)
B \(14\times21\)
C \(2\times147\)
D \(6\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times7^2\)
Step 1
Concept
\(294=6\times49\) लिखें। / Write \(294=6\times49\).
Step 2
Why this answer is correct
\(6=2\times3\) और \(49=7^2\), इसलिए \(294=2\times3\times7^2\)। / \(6=2\times3\) and \(49=7^2\), so \(294=2\times3\times7^2\).
Step 3
Exam Tip
49 को \(7^2\) के रूप में लिखें। / Write 49 as \(7^2\).
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संख्या 300 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 300?
#prime-factorisation
#number-300
#easy
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A \(2^2\times3\times5^2\)
B \(30\times10\)
C \(3\times100\)
D \(2\times150\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times5^2\)
Step 1
Concept
\(300=3\times100\) लिखें। / Write \(300=3\times100\).
Step 2
Why this answer is correct
\(100=2^2\times5^2\), इसलिए \(300=2^2\times3\times5^2\)। / \(100=2^2\times5^2\), so \(300=2^2\times3\times5^2\).
Step 3
Exam Tip
100 को अभाज्य घातों में बदलें। / Convert 100 into prime powers.
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संख्या 315 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 315?
#prime-factorisation
#number-315
#easy
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? Hint Small clue
A \(3^2\times5\times7\)
B \(9\times35\)
C \(3\times105\)
D \(15\times21\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5\times7\)
Step 1
Concept
\(315=9\times35\) लिखें। / Write \(315=9\times35\).
Step 2
Why this answer is correct
\(9=3^2\) और \(35=5\times7\), इसलिए \(315=3^2\times5\times7\)। / \(9=3^2\) and \(35=5\times7\), so \(315=3^2\times5\times7\).
Step 3
Exam Tip
9 और 35 दोनों को अभाज्य रूप में बदलें। / Change both 9 and 35 into prime form.
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संख्या 324 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 324?
#prime-factorisation
#number-324
#easy
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? Hint Small clue
A \(2^2\times3^4\)
B \(18\times18\)
C \(4\times81\)
D \(2^4\times3^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^4\)
Step 1
Concept
\(324=4\times81\) लिखें। / Write \(324=4\times81\).
Step 2
Why this answer is correct
\(4=2^2\) और \(81=3^4\), इसलिए \(324=2^2\times3^4\)। / \(4=2^2\) and \(81=3^4\), so \(324=2^2\times3^4\).
Step 3
Exam Tip
वर्ग संख्या होने पर घातों को ध्यान से जांचें। / Since it is a square number, check powers carefully.
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संख्या 330 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 330?
#prime-factorisation
#number-330
#easy
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? Hint Small clue
A \(2\times3\times5\times11\)
B \(33\times10\)
C \(30\times11\)
D \(6\times55\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\times11\)
Step 1
Concept
\(330=33\times10\) लिखें। / Write \(330=33\times10\).
Step 2
Why this answer is correct
\(33=3\times11\) और \(10=2\times5\), इसलिए \(330=2\times3\times5\times11\)। / \(33=3\times11\) and \(10=2\times5\), so \(330=2\times3\times5\times11\).
Step 3
Exam Tip
सभी संयुक्त गुणनखंडों को आगे तोड़ें। / Break all composite factors further.
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संख्या 343 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 343?
#prime-factorisation
#cube-number
#easy
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? Hint Small clue
A \(7^3\)
B \(7^2\)
C \(49\times7\)
D \(343\times1\)
Explanation opens after your attempt
Correct Answer
A. \(7^3\)
Step 1
Concept
\(343=7\times49\) लिखें। / Write \(343=7\times49\).
Step 2
Why this answer is correct
\(49=7^2\), इसलिए \(343=7^3\)। / Since \(49=7^2\), \(343=7^3\).
Step 3
Exam Tip
49 संयुक्त है, इसलिए अंतिम रूप में \(7^3\) लिखें। / 49 is composite, so write \(7^3\) in the final form.
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संख्या 360 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 360?
#prime-factorisation
#number-360
#easy
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? Hint Small clue
A \(2^3\times3^2\times5\)
B \(36\times10\)
C \(2^2\times3\times30\)
D \(12\times30\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\)
Step 1
Concept
\(360=36\times10\) लिखें। / Write \(360=36\times10\).
Step 2
Why this answer is correct
\(36=2^2\times3^2\) और \(10=2\times5\), इसलिए \(360=2^3\times3^2\times5\)। / \(36=2^2\times3^2\) and \(10=2\times5\), so \(360=2^3\times3^2\times5\).
Step 3
Exam Tip
2 की कुल घात गिनते समय सावधानी रखें। / Be careful while counting the total power of 2.
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संख्या 375 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 375?
#prime-factorisation
#number-375
#easy
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+10 Time+ 10 sec extra
? Hint Small clue
A \(3\times5^3\)
B \(15\times25\)
C \(3^2\times5^2\)
D \(75\times5\)
Explanation opens after your attempt
Correct Answer
A. \(3\times5^3\)
Step 1
Concept
\(375=3\times125\) लिखें। / Write \(375=3\times125\).
Step 2
Why this answer is correct
\(125=5^3\), इसलिए \(375=3\times5^3\)। / Since \(125=5^3\), \(375=3\times5^3\).
Step 3
Exam Tip
125 को \(5^3\) में बदलें। / Change 125 into \(5^3\).
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संख्या 392 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 392?
#prime-factorisation
#number-392
#easy
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^3\times7^2\)
B \(8\times49\)
C \(2^2\times98\)
D \(14\times28\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times7^2\)
Step 1
Concept
\(392=8\times49\) लिखें। / Write \(392=8\times49\).
Step 2
Why this answer is correct
\(8=2^3\) और \(49=7^2\), इसलिए \(392=2^3\times7^2\)। / \(8=2^3\) and \(49=7^2\), so \(392=2^3\times7^2\).
Step 3
Exam Tip
8 और 49 को अभाज्य घातों में बदलें। / Convert 8 and 49 into prime powers.
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संख्या 400 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 400?
#prime-factorisation
#number-400
#easy
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^4\times5^2\)
B \(20\times20\)
C \(4\times100\)
D \(2^2\times10^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times5^2\)
Step 1
Concept
\(400=16\times25\) लिखें। / Write \(400=16\times25\).
Step 2
Why this answer is correct
\(16=2^4\) और \(25=5^2\), इसलिए \(400=2^4\times5^2\)। / \(16=2^4\) and \(25=5^2\), so \(400=2^4\times5^2\).
Step 3
Exam Tip
20 या 10 जैसे संयुक्त रूप अंतिम उत्तर नहीं होते। / Composite forms like 20 or 10 are not final answers.
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संख्या 441 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 441?
#prime-factorisation
#square-number
#easy
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A \(3^2\times7^2\)
B \(21\times21\)
C \(9\times49\)
D \(3\times147\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times7^2\)
Step 1
Concept
\(441=21^2\) पहचाना जा सकता है। / Recognise \(441=21^2\).
Step 2
Why this answer is correct
\(21=3\times7\), इसलिए \(441=3^2\times7^2\)। / Since \(21=3\times7\), \(441=3^2\times7^2\).
Step 3
Exam Tip
21 संयुक्त है, इसलिए अभाज्य आधार 3 और 7 लिखें। / 21 is composite, so write prime bases 3 and 7.
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संख्या 450 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 450?
#prime-factorisation
#number-450
#easy
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A \(2\times3^2\times5^2\)
B \(45\times10\)
C \(2^2\times3^2\times5\)
D \(9\times50\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5^2\)
Step 1
Concept
\(450=45\times10\) लिखें। / Write \(450=45\times10\).
Step 2
Why this answer is correct
\(45=3^2\times5\) और \(10=2\times5\), इसलिए \(450=2\times3^2\times5^2\)। / \(45=3^2\times5\) and \(10=2\times5\), so \(450=2\times3^2\times5^2\).
Step 3
Exam Tip
5 दो बार आता है, इसलिए \(5^2\) लिखें। / Since 5 appears twice, write \(5^2\).
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संख्या 480 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 480?
#prime-factorisation
#number-480
#easy
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A \(2^5\times3\times5\)
B \(48\times10\)
C \(2^4\times30\)
D \(16\times30\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3\times5\)
Step 1
Concept
\(480=48\times10\) लिखें। / Write \(480=48\times10\).
Step 2
Why this answer is correct
\(48=2^4\times3\) और \(10=2\times5\), इसलिए \(480=2^5\times3\times5\)। / \(48=2^4\times3\) and \(10=2\times5\), so \(480=2^5\times3\times5\).
Step 3
Exam Tip
2 की कुल घात सही गिनें। / Count the total power of 2 correctly.
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यदि \(132=2^a\times3\times11\), तो (a) का मान क्या है?
If \(132=2^a\times3\times11\), what is the value of (a)?
#exponent-comparison
#prime-factorisation
#easy
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A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
132 का अभाज्य गुणनखंडन \(2^2\times3\times11\) है। / The prime factorisation of 132 is \(2^2\times3\times11\).
Step 2
Why this answer is correct
दिए गए रूप में 2 की घात (a) है। / In the given form, the power of 2 is (a).
Step 3
Exam Tip
तुलना करने पर (a=2) मिलता है। / Comparing gives (a=2).
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यदि \(150=2\times3\times5^b\), तो (b) का मान क्या है?
If \(150=2\times3\times5^b\), what is the value of (b)?
#exponent-comparison
#prime-factorisation
#easy
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A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
150 का अभाज्य गुणनखंडन \(2\times3\times5^2\) है। / The prime factorisation of 150 is \(2\times3\times5^2\).
Step 2
Why this answer is correct
दिए गए रूप में 5 की घात (b) है। / In the given form, the power of 5 is (b).
Step 3
Exam Tip
तुलना करने पर (b=2) है। / Comparing gives (b=2).
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times3\times7\) है?
Which number has prime factorisation \(2^3\times3\times7\)?
#evaluate-factorisation
#number-168
#easy
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A 168
B 84
C 126
D 336
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) निकालें। / Calculate \(2^3=8\).
Step 2
Why this answer is correct
\(8\times3\times7=168\)। / \(8\times3\times7=168\).
Step 3
Exam Tip
अभाज्य गुणनखंडन से संख्या पाने के लिए सभी गुणनखंडों को गुणा करें। / To get the number from prime factorisation, multiply all factors.
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किस संख्या का अभाज्य गुणनखंडन \(2\times3^3\times5\) है?
Which number has prime factorisation \(2\times3^3\times5\)?
#evaluate-factorisation
#number-270
#easy
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A 270
B 180
C 135
D 540
Explanation opens after your attempt
Step 1
Concept
\(3^3=27\) निकालें। / Calculate \(3^3=27\).
Step 2
Why this answer is correct
\(2\times27\times5=270\)। / \(2\times27\times5=270\).
Step 3
Exam Tip
घात का मान पहले निकालने से गणना आसान होती है। / Evaluating the power first makes calculation easy.
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यदि \(n=2^4\times3\times5\), तो (n) का मान क्या है?
If \(n=2^4\times3\times5\), what is the value of (n)?
#evaluate-factorisation
#powers
#easy
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A 240
B 120
C 180
D 300
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) है। / \(2^4=16\).
Step 2
Why this answer is correct
\(16\times3\times5=240\)। / \(16\times3\times5=240\).
Step 3
Exam Tip
अभाज्य रूप से संख्या पाने के लिए गुणा करें। / Multiply to get the number from prime form.
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यदि \(m=3^2\times5\times7\), तो (m) का मान क्या है?
If \(m=3^2\times5\times7\), what is the value of (m)?
#evaluate-factorisation
#powers
#easy
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A 315
B 210
C 175
D 420
Explanation opens after your attempt
Step 1
Concept
\(3^2=9\) निकालें। / Calculate \(3^2=9\).
Step 2
Why this answer is correct
\(9\times5\times7=315\)। / \(9\times5\times7=315\).
Step 3
Exam Tip
घात वाले गुणनखंड को पहले सरल करें। / Simplify the factor with a power first.
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किस विकल्प में केवल अभाज्य गुणनखंड दिए गए हैं?
Which option contains only prime factors?
#prime-factors
#concept-check
#easy
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A \(2\times3\times7\times11\)
B \(6\times7\times11\)
C \(21\times11\)
D \(2\times33\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times7\times11\)
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में हर गुणनखंड अभाज्य होना चाहिए। / In final prime factorisation, every factor must be prime.
Step 2
Why this answer is correct
2, 3, 7 और 11 सभी अभाज्य हैं। / 2, 3, 7, and 11 are all prime.
Step 3
Exam Tip
6, 21 और 33 संयुक्त हैं, इसलिए वे अंतिम रूप में नहीं रह सकते। / 6, 21, and 33 are composite, so they cannot remain in final form.
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किस विकल्प में अंतिम अभाज्य गुणनखंडन नहीं दिया गया है?
Which option is not a final prime factorisation?
#prime-factorisation
#not-final-form
#easy
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A \(6\times5^2\)
B \(2\times3\times5^2\)
C \(2^2\times3\times7\)
D \(3^2\times5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(6\times5^2\)
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में संयुक्त गुणनखंड नहीं होना चाहिए। / Final prime factorisation must not contain a composite factor.
Step 2
Why this answer is correct
6 संयुक्त संख्या है, इसलिए \(6\times5^2\) अंतिम रूप नहीं है। / 6 is composite, so \(6\times5^2\) is not final form.
Step 3
Exam Tip
6 को \(2\times3\) में बदलें। / Change 6 into \(2\times3\).
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संख्या 256 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 256?
#prime-factorisation
#power-of-two
#easy
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A \(2^8\)
B \(2^7\)
C \(4^4\)
D \(16^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^8\)
Step 1
Concept
256 को बार-बार 2 से भाग दें। / Divide 256 repeatedly by 2.
Step 2
Why this answer is correct
आठ बार 2 मिलने से \(256=2^8\) होता है। / Eight factors of 2 give \(256=2^8\).
Step 3
Exam Tip
4 और 16 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप में न लिखें। / 4 and 16 are composite, so do not write them in final prime form.
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संख्या 243 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 243?
#prime-factorisation
#power-of-three
#easy
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A \(3^5\)
B \(3^4\)
C \(9^3\)
D \(27\times9\)
Explanation opens after your attempt
Correct Answer
A. \(3^5\)
Step 1
Concept
243 को 3 से बार-बार भाग दें। / Divide 243 repeatedly by 3.
Step 2
Why this answer is correct
पांच बार 3 मिलने से \(243=3^5\)। / Five factors of 3 give \(243=3^5\).
Step 3
Exam Tip
9 और 27 संयुक्त हैं, इसलिए अभाज्य आधार 3 रखें। / 9 and 27 are composite, so keep prime base 3.
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संख्या 169 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 169?
#prime-factorisation
#square-number
#easy
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A \(13^2\)
B \(13\times12\)
C \(169\times1\)
D \(7\times24\)
Explanation opens after your attempt
Correct Answer
A. \(13^2\)
Step 1
Concept
169 एक वर्ग संख्या है। / 169 is a square number.
Step 2
Why this answer is correct
\(169=13\times13=13^2\)। / \(169=13\times13=13^2\).
Step 3
Exam Tip
13 अभाज्य है, इसलिए \(13^2\) सही अभाज्य गुणनखंडन है। / Since 13 is prime, \(13^2\) is the correct prime factorisation.
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संख्या 289 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 289?
#prime-factorisation
#square-number
#easy
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A \(17^2\)
B \(17\times18\)
C \(289\times1\)
D \(13\times22\)
Explanation opens after your attempt
Correct Answer
A. \(17^2\)
Step 1
Concept
\(289=17\times17\) है। / \(289=17\times17\).
Step 2
Why this answer is correct
17 अभाज्य संख्या है, इसलिए \(289=17^2\)। / Since 17 is prime, \(289=17^2\).
Step 3
Exam Tip
वर्ग संख्या में समान अभाज्य दो बार आता है। / In a square number, the same prime appears twice.
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संख्या 512 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 512?
#prime-factorisation
#power-of-two
#easy
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A \(2^9\)
B \(2^8\)
C \(8^3\)
D \(16\times32\)
Explanation opens after your attempt
Correct Answer
A. \(2^9\)
Step 1
Concept
512 को बार-बार 2 से भाग दें। / Divide 512 repeatedly by 2.
Step 2
Why this answer is correct
नौ बार 2 मिलने से \(512=2^9\)। / Nine factors of 2 give \(512=2^9\).
Step 3
Exam Tip
8, 16 और 32 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप में 2 की घात लिखें। / 8, 16, and 32 are composite, so write the power of 2 in final prime form.
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संख्या 625 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 625?
#prime-factorisation
#power-of-five
#easy
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A \(5^4\)
B \(25^2\)
C \(5^3\)
D \(125\times5\)
Explanation opens after your attempt
Correct Answer
A. \(5^4\)
Step 1
Concept
\(625=25\times25\) लिखा जा सकता है। / (625) can be written as \(25\times25\).
Step 2
Why this answer is correct
\(25=5^2\), इसलिए \(625=5^4\)। / \(25=5^2\), so \(625=5^4\).
Step 3
Exam Tip
25 संयुक्त है, इसलिए अंतिम रूप में 5 की घात लिखें। / 25 is composite, so write the power of 5 in final form.
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संख्या 216 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 216?
#prime-factorisation
#cube-number
#easy
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A \(2^3\times3^3\)
B \(6^3\)
C \(8\times27\)
D \(2^4\times3^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\)
Step 1
Concept
\(216=8\times27\) लिखें। / Write \(216=8\times27\).
Step 2
Why this answer is correct
\(8=2^3\) और \(27=3^3\), इसलिए \(216=2^3\times3^3\)। / \(8=2^3\) and \(27=3^3\), so \(216=2^3\times3^3\).
Step 3
Exam Tip
6, 8 और 27 संयुक्त हैं, इसलिए अंतिम रूप में अभाज्य आधार लिखें। / 6, 8, and 27 are composite, so write prime bases in final form.
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संख्या 128 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 128?
#prime-factorisation
#power-of-two
#easy
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A \(2^7\)
B \(2^6\)
C \(4^3\)
D \(8\times16\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\)
Step 1
Concept
128 को बार-बार 2 से भाग दें। / Divide 128 repeatedly by 2.
Step 2
Why this answer is correct
सात बार 2 मिलने से \(128=2^7\)। / Seven factors of 2 give \(128=2^7\).
Step 3
Exam Tip
4, 8 और 16 संयुक्त हैं, इसलिए अंतिम रूप में \(2^7\) लिखें। / 4, 8, and 16 are composite, so write \(2^7\) in final form.
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संख्या 540 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 540?
#prime-factorisation
#number-540
#easy
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A \(2^2\times3^3\times5\)
B \(54\times10\)
C \(2\times270\)
D \(6\times90\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\times5\)
Step 1
Concept
\(540=54\times10\) लिखें। / Write \(540=54\times10\).
Step 2
Why this answer is correct
\(54=2\times3^3\) और \(10=2\times5\), इसलिए \(540=2^2\times3^3\times5\)। / \(54=2\times3^3\) and \(10=2\times5\), so \(540=2^2\times3^3\times5\).
Step 3
Exam Tip
54 को पूरी तरह अभाज्य रूप में तोड़ें। / Break 54 completely into prime form.
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संख्या 588 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 588?
#prime-factorisation
#number-588
#easy
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? Hint Small clue
A \(2^2\times3\times7^2\)
B \(12\times49\)
C \(6\times98\)
D \(2\times294\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times7^2\)
Step 1
Concept
\(588=12\times49\) लिखें। / Write \(588=12\times49\).
Step 2
Why this answer is correct
\(12=2^2\times3\) और \(49=7^2\), इसलिए \(588=2^2\times3\times7^2\)। / \(12=2^2\times3\) and \(49=7^2\), so \(588=2^2\times3\times7^2\).
Step 3
Exam Tip
12 और 49 को अभाज्य घातों में बदलें। / Convert 12 and 49 into prime powers.
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संख्या 660 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 660?
#prime-factorisation
#number-660
#easy
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? Hint Small clue
A \(2^2\times3\times5\times11\)
B \(66\times10\)
C \(6\times110\)
D \(22\times30\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times5\times11\)
Step 1
Concept
\(660=66\times10\) लिखें। / Write \(660=66\times10\).
Step 2
Why this answer is correct
\(66=2\times3\times11\) और \(10=2\times5\), इसलिए \(660=2^2\times3\times5\times11\)। / \(66=2\times3\times11\) and \(10=2\times5\), so \(660=2^2\times3\times5\times11\).
Step 3
Exam Tip
2 दो बार आता है, इसलिए \(2^2\) लिखें। / Since 2 appears twice, write \(2^2\).
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^2\times3\times11\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^2\times3\times11\), which number is it?
#evaluate-factorisation
#number-132
#easy
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A 132
B 66
C 264
D 99
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\) निकालें। / Calculate \(2^2=4\).
Step 2
Why this answer is correct
\(4\times3\times11=132\)। / \(4\times3\times11=132\).
Step 3
Exam Tip
अभाज्य गुणनखंडन से संख्या पाने के लिए सभी गुणनखंडों का गुणा करें। / Multiply all factors to get the number from prime factorisation.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(3^2\times5^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(3^2\times5^2\), which number is it?
#evaluate-factorisation
#number-225
#easy
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A 225
B 150
C 300
D 450
Explanation opens after your attempt
Step 1
Concept
\(3^2=9\) और \(5^2=25\) निकालें। / Calculate \(3^2=9\) and \(5^2=25\).
Step 2
Why this answer is correct
\(9\times25=225\)। / \(9\times25=225\).
Step 3
Exam Tip
घातों को पहले सरल करें, फिर गुणा करें। / Simplify powers first and then multiply.
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किस संख्या का अभाज्य गुणनखंडन \(2\times3\times5\times7\) है?
Which number has prime factorisation \(2\times3\times5\times7\)?
#evaluate-factorisation
#number-210
#easy
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A 210
B 105
C 420
D 315
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Step 1
Concept
सभी अभाज्य गुणनखंड दिए हैं। / All prime factors are given.
Step 2
Why this answer is correct
\(2\times3\times5\times7=210\)। / \(2\times3\times5\times7=210\).
Step 3
Exam Tip
जब घात न हो तो हर अभाज्य एक बार लिया जाता है। / When no power is written, each prime is taken once.
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किस संख्या का अभाज्य गुणनखंडन \(2^2\times3^2\times7\) है?
Which number has prime factorisation \(2^2\times3^2\times7\)?
#evaluate-factorisation
#number-252
#easy
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A 252
B 126
C 504
D 378
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\) और \(3^2=9\) निकालें। / Calculate \(2^2=4\) and \(3^2=9\).
Step 2
Why this answer is correct
\(4\times9\times7=252\)। / \(4\times9\times7=252\).
Step 3
Exam Tip
अभाज्य घातों का मान निकालकर गुणा करें। / Evaluate prime powers and then multiply.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4\times5^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^4\times5^2\), which number is it?
#evaluate-factorisation
#number-400
#easy
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A 400
B 200
C 800
D 100
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(5^2=25\) निकालें। / Calculate \(2^4=16\) and \(5^2=25\).
Step 2
Why this answer is correct
\(16\times25=400\)। / \(16\times25=400\).
Step 3
Exam Tip
घातों का मान पहले निकालना आसान रहता है। / Finding powers first makes the calculation easier.
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अभाज्य गुणनखंडन करते समय 1 को अंतिम अभाज्य गुणनखंड क्यों नहीं लिखा जाता?
Why is 1 not written as a final prime factor during prime factorisation?
#prime-factorisation
#one-not-prime
#easy
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A क्योंकि 1 अभाज्य संख्या नहीं है / Because 1 is not a prime number
B क्योंकि 1 सबसे बड़ी संख्या है / Because 1 is the largest number
C क्योंकि 1 हमेशा सम संख्या है / Because 1 is always even
D क्योंकि 1 केवल 2 से विभाज्य है / Because 1 is divisible only by 2
Explanation opens after your attempt
Correct Answer
A. क्योंकि 1 अभाज्य संख्या नहीं है / Because 1 is not a prime number
Step 1
Concept
अभाज्य संख्या के ठीक दो गुणनखंड होते हैं। / A prime number has exactly two factors.
Step 2
Why this answer is correct
1 का केवल एक ही गुणनखंड है, इसलिए 1 अभाज्य नहीं है। / 1 has only one factor, so 1 is not prime.
Step 3
Exam Tip
अभाज्य गुणनखंडन में 1 को अंतिम गुणनखंड न लिखें। / Do not write 1 as a final factor in prime factorisation.
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