अभाज्य गुणनखंडन में अंतिम रूप की सबसे जरूरी शर्त क्या होती है?
What is the most important condition for the final form of prime factorisation?
#prime-factorisation
#concept
#medium
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A सभी गुणनखंड अभाज्य होने चाहिए / All factors must be prime
B सभी गुणनखंड सम होने चाहिए / All factors must be even
C सभी गुणनखंड दो अंकों के होने चाहिए / All factors must be two-digit numbers
D गुणनखंडों का योग संख्या के बराबर होना चाहिए / Sum of factors must equal the number
Explanation opens after your attempt
Correct Answer
A. सभी गुणनखंड अभाज्य होने चाहिए / All factors must be prime
Step 1
Concept
अभाज्य गुणनखंडन में संख्या को अभाज्य संख्याओं के गुणनफल में लिखा जाता है। / In prime factorisation, a number is written as a product of prime numbers.
Step 2
Why this answer is correct
यदि कोई संयुक्त गुणनखंड बचा है, तो रूप अंतिम नहीं माना जाएगा। / If any composite factor remains, the form is not final.
Step 3
Exam Tip
परीक्षा में अंतिम उत्तर में केवल अभाज्य आधार और उनकी घातें लिखें। / In exams, write only prime bases and their powers in the final answer.
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संख्या 504 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 504?
#prime-factorisation
#number-504
#medium
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A \(2^3\times3^2\times7\)
B \(2^2\times3^3\times7\)
C \(8\times63\)
D \(2^3\times9\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times7\)
Step 1
Concept
\(504=8\times63\) लिखें। / Write \(504=8\times63\).
Step 2
Why this answer is correct
\(8=2^3\) और \(63=3^2\times7\), इसलिए \(504=2^3\times3^2\times7\)। / \(8=2^3\) and \(63=3^2\times7\), so \(504=2^3\times3^2\times7\).
Step 3
Exam Tip
8 और 63 जैसे संयुक्त रूपों को अंतिम उत्तर में न छोड़ें। / Do not leave composite forms like 8 and 63 in the final answer.
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संख्या 528 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 528?
#prime-factorisation
#number-528
#medium
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A \(2^4\times3\times11\)
B \(2^3\times3\times22\)
C \(16\times33\)
D \(2^4\times33\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3\times11\)
Step 1
Concept
\(528=16\times33\) लिखा जा सकता है। / (528) can be written as \(16\times33\).
Step 2
Why this answer is correct
\(16=2^4\) और \(33=3\times11\), इसलिए \(528=2^4\times3\times11\)। / \(16=2^4\) and \(33=3\times11\), so \(528=2^4\times3\times11\).
Step 3
Exam Tip
33 संयुक्त है, इसलिए उसे 3 और 11 में तोड़ें। / Since 33 is composite, split it into 3 and 11.
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संख्या 560 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 560?
#prime-factorisation
#number-560
#medium
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A \(2^4\times5\times7\)
B \(2^3\times5\times14\)
C \(16\times35\)
D \(2^4\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times5\times7\)
Step 1
Concept
\(560=16\times35\) लिखें। / Write \(560=16\times35\).
Step 2
Why this answer is correct
\(16=2^4\) और \(35=5\times7\), इसलिए \(560=2^4\times5\times7\)। / \(16=2^4\) and \(35=5\times7\), so \(560=2^4\times5\times7\).
Step 3
Exam Tip
35 संयुक्त है, इसलिए अंतिम रूप में 5 और 7 लिखें। / Since 35 is composite, write 5 and 7 in the final form.
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संख्या 630 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 630?
#prime-factorisation
#number-630
#medium
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A \(2\times3^2\times5\times7\)
B \(2^2\times3\times5\times7\)
C \(63\times10\)
D \(2\times9\times35\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\times7\)
Step 1
Concept
\(630=63\times10\) लिखें। / Write \(630=63\times10\).
Step 2
Why this answer is correct
\(63=3^2\times7\) और \(10=2\times5\), इसलिए \(630=2\times3^2\times5\times7\)। / \(63=3^2\times7\) and \(10=2\times5\), so \(630=2\times3^2\times5\times7\).
Step 3
Exam Tip
9 और 35 को अंतिम रूप में न रखें। / Do not keep 9 or 35 in the final form.
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संख्या 672 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 672?
#prime-factorisation
#number-672
#medium
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A \(2^5\times3\times7\)
B \(2^4\times3\times7\)
C \(32\times21\)
D \(2^5\times21\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3\times7\)
Step 1
Concept
\(672=32\times21\) लिखा जा सकता है। / (672) can be written as \(32\times21\).
Step 2
Why this answer is correct
\(32=2^5\) और \(21=3\times7\), इसलिए \(672=2^5\times3\times7\)। / \(32=2^5\) and \(21=3\times7\), so \(672=2^5\times3\times7\).
Step 3
Exam Tip
21 संयुक्त है, इसलिए उसे आगे तोड़ें। / Since 21 is composite, break it further.
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संख्या 700 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 700?
#prime-factorisation
#number-700
#medium
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A \(2^2\times5^2\times7\)
B \(2\times5^2\times14\)
C \(7\times100\)
D \(4\times175\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times5^2\times7\)
Step 1
Concept
\(700=7\times100\) लिखें। / Write \(700=7\times100\).
Step 2
Why this answer is correct
\(100=2^2\times5^2\), इसलिए \(700=2^2\times5^2\times7\)। / \(100=2^2\times5^2\), so \(700=2^2\times5^2\times7\).
Step 3
Exam Tip
100 को अभाज्य घातों में बदलना जरूरी है। / It is necessary to change 100 into prime powers.
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संख्या 756 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 756?
#prime-factorisation
#number-756
#medium
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A \(2^2\times3^3\times7\)
B \(2^3\times3^2\times7\)
C \(27\times28\)
D \(4\times189\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\times7\)
Step 1
Concept
\(756=27\times28\) लिखें। / Write \(756=27\times28\).
Step 2
Why this answer is correct
\(27=3^3\) और \(28=2^2\times7\), इसलिए \(756=2^2\times3^3\times7\)। / \(27=3^3\) and \(28=2^2\times7\), so \(756=2^2\times3^3\times7\).
Step 3
Exam Tip
दोनों भागों को पूरा अभाज्य रूप दें। / Give complete prime form to both parts.
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संख्या 945 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 945?
#prime-factorisation
#number-945
#medium
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A \(3^3\times5\times7\)
B \(3^2\times5\times7\)
C \(27\times35\)
D \(9\times105\)
Explanation opens after your attempt
Correct Answer
A. \(3^3\times5\times7\)
Step 1
Concept
\(945=27\times35\) लिखें। / Write \(945=27\times35\).
Step 2
Why this answer is correct
\(27=3^3\) और \(35=5\times7\), इसलिए \(945=3^3\times5\times7\)। / \(27=3^3\) and \(35=5\times7\), so \(945=3^3\times5\times7\).
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 980 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 980?
#prime-factorisation
#number-980
#medium
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A \(2^2\times5\times7^2\)
B \(2\times5\times7^2\)
C \(98\times10\)
D \(4\times245\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times5\times7^2\)
Step 1
Concept
\(980=98\times10\) लिखें। / Write \(980=98\times10\).
Step 2
Why this answer is correct
\(98=2\times7^2\) और \(10=2\times5\), इसलिए \(980=2^2\times5\times7^2\)। / \(98=2\times7^2\) and \(10=2\times5\), so \(980=2^2\times5\times7^2\).
Step 3
Exam Tip
2 की कुल घात सही गिनें। / Count the total power of 2 correctly.
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संख्या 1008 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1008?
#prime-factorisation
#number-1008
#medium
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A \(2^4\times3^2\times7\)
B \(2^3\times3^2\times7\)
C \(16\times63\)
D \(2^4\times63\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^2\times7\)
Step 1
Concept
\(1008=16\times63\) लिखें। / Write \(1008=16\times63\).
Step 2
Why this answer is correct
\(16=2^4\) और \(63=3^2\times7\), इसलिए \(1008=2^4\times3^2\times7\)। / \(16=2^4\) and \(63=3^2\times7\), so \(1008=2^4\times3^2\times7\).
Step 3
Exam Tip
63 को पूरा अभाज्य रूप दें। / Give 63 its complete prime form.
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संख्या 1155 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1155?
#prime-factorisation
#number-1155
#medium
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A \(3\times5\times7\times11\)
B \(11\times105\)
C \(3\times385\)
D \(15\times77\)
Explanation opens after your attempt
Correct Answer
A. \(3\times5\times7\times11\)
Step 1
Concept
\(1155=11\times105\) लिखें। / Write \(1155=11\times105\).
Step 2
Why this answer is correct
\(105=3\times5\times7\), इसलिए \(1155=3\times5\times7\times11\)। / \(105=3\times5\times7\), so \(1155=3\times5\times7\times11\).
Step 3
Exam Tip
105 संयुक्त है, इसलिए उसे आगे तोड़ें। / Since 105 is composite, break it further.
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संख्या 1176 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1176?
#prime-factorisation
#number-1176
#medium
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A \(2^3\times3\times7^2\)
B \(2^2\times3^2\times7^2\)
C \(24\times49\)
D \(12\times98\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times7^2\)
Step 1
Concept
\(1176=24\times49\) लिखें। / Write \(1176=24\times49\).
Step 2
Why this answer is correct
\(24=2^3\times3\) और \(49=7^2\), इसलिए \(1176=2^3\times3\times7^2\)। / \(24=2^3\times3\) and \(49=7^2\), so \(1176=2^3\times3\times7^2\).
Step 3
Exam Tip
24 और 49 को अभाज्य घातों में बदलें। / Convert 24 and 49 into prime powers.
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संख्या 1225 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1225?
#prime-factorisation
#square-number
#medium
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A \(5^2\times7^2\)
B \(35\times35\)
C \(5\times245\)
D \(7\times175\)
Explanation opens after your attempt
Correct Answer
A. \(5^2\times7^2\)
Step 1
Concept
\(1225=35^2\) पहचाना जा सकता है। / Recognise \(1225=35^2\).
Step 2
Why this answer is correct
\(35=5\times7\), इसलिए \(1225=5^2\times7^2\)। / Since \(35=5\times7\), \(1225=5^2\times7^2\).
Step 3
Exam Tip
वर्ग संख्या में अभाज्य घातें सम मिल सकती हैं। / In a square number, prime exponents may be even.
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संख्या 1296 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1296?
#prime-factorisation
#number-1296
#medium
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A \(2^4\times3^4\)
B \(2^3\times3^5\)
C \(36\times36\)
D \(16\times81\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^4\)
Step 1
Concept
\(1296=16\times81\) लिखें। / Write \(1296=16\times81\).
Step 2
Why this answer is correct
\(16=2^4\) और \(81=3^4\), इसलिए \(1296=2^4\times3^4\)। / \(16=2^4\) and \(81=3^4\), so \(1296=2^4\times3^4\).
Step 3
Exam Tip
16 और 81 को अंतिम उत्तर में न छोड़ें। / Do not leave 16 and 81 in the final answer.
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संख्या 1323 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1323?
#prime-factorisation
#number-1323
#medium
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A \(3^3\times7^2\)
B \(3^2\times7^3\)
C \(27\times49\)
D \(21\times63\)
Explanation opens after your attempt
Correct Answer
A. \(3^3\times7^2\)
Step 1
Concept
\(1323=27\times49\) लिखें। / Write \(1323=27\times49\).
Step 2
Why this answer is correct
\(27=3^3\) और \(49=7^2\), इसलिए \(1323=3^3\times7^2\)। / \(27=3^3\) and \(49=7^2\), so \(1323=3^3\times7^2\).
Step 3
Exam Tip
27 और 49 दोनों संयुक्त हैं, इसलिए अभाज्य घातों में लिखें। / Both 27 and 49 are composite, so write them as prime powers.
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संख्या 1440 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1440?
#prime-factorisation
#number-1440
#medium
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? Hint Small clue
A \(2^5\times3^2\times5\)
B \(2^4\times3^2\times5\)
C \(144\times10\)
D \(32\times45\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^2\times5\)
Step 1
Concept
\(1440=144\times10\) लिखें। / Write \(1440=144\times10\).
Step 2
Why this answer is correct
\(144=2^4\times3^2\) और \(10=2\times5\), इसलिए \(1440=2^5\times3^2\times5\)। / \(144=2^4\times3^2\) and \(10=2\times5\), so \(1440=2^5\times3^2\times5\).
Step 3
Exam Tip
2 की कुल घात 5 है। / The total power of 2 is 5.
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संख्या 1470 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1470?
#prime-factorisation
#number-1470
#medium
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? Hint Small clue
A \(2\times3\times5\times7^2\)
B \(2^2\times3\times5\times7\)
C \(30\times49\)
D \(14\times105\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\times7^2\)
Step 1
Concept
\(1470=30\times49\) लिखें। / Write \(1470=30\times49\).
Step 2
Why this answer is correct
\(30=2\times3\times5\) और \(49=7^2\), इसलिए \(1470=2\times3\times5\times7^2\)। / \(30=2\times3\times5\) and \(49=7^2\), so \(1470=2\times3\times5\times7^2\).
Step 3
Exam Tip
49 को \(7^2\) के रूप में लिखें। / Write 49 as \(7^2\).
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संख्या 1728 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1728?
#prime-factorisation
#cube-number
#medium
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? Hint Small clue
A \(2^6\times3^3\)
B \(2^5\times3^4\)
C \(12^3\)
D \(64\times27\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^3\)
Step 1
Concept
\(1728=12^3\) पहचाना जा सकता है। / Recognise \(1728=12^3\).
Step 2
Why this answer is correct
\(12=2^2\times3\), इसलिए \(12^3=2^6\times3^3\)। / Since \(12=2^2\times3\), \(12^3=2^6\times3^3\).
Step 3
Exam Tip
12 संयुक्त है, इसलिए अंतिम रूप में 2 और 3 की घातें लिखें। / Since 12 is composite, write powers of 2 and 3 in the final form.
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संख्या 1800 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1800?
#prime-factorisation
#number-1800
#medium
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A \(2^3\times3^2\times5^2\)
B \(2^2\times3^2\times5^2\)
C \(18\times100\)
D \(2\times900\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5^2\)
Step 1
Concept
\(1800=18\times100\) लिखें। / Write \(1800=18\times100\).
Step 2
Why this answer is correct
\(18=2\times3^2\) और \(100=2^2\times5^2\), इसलिए \(1800=2^3\times3^2\times5^2\)। / \(18=2\times3^2\) and \(100=2^2\times5^2\), so \(1800=2^3\times3^2\times5^2\).
Step 3
Exam Tip
18 और 100 दोनों को पूरा अभाज्य रूप दें। / Give complete prime form to both 18 and 100.
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संख्या 1980 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1980?
#prime-factorisation
#number-1980
#medium
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? Hint Small clue
A \(2^2\times3^2\times5\times11\)
B \(2\times3^2\times5\times11\)
C \(198\times10\)
D \(18\times110\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times5\times11\)
Step 1
Concept
\(1980=198\times10\) लिखें। / Write \(1980=198\times10\).
Step 2
Why this answer is correct
\(198=2\times3^2\times11\) और \(10=2\times5\), इसलिए \(1980=2^2\times3^2\times5\times11\)। / \(198=2\times3^2\times11\) and \(10=2\times5\), so \(1980=2^2\times3^2\times5\times11\).
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 \(840=2^a\times3\times5\times7\), तो (a) का मान क्या है?
If \(840=2^a\times3\times5\times7\), what is the value of (a)?
#exponent-comparison
#prime-factorisation
#medium
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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
\(840=84\times10\) है। / \(840=84\times10\).
Step 2
Why this answer is correct
\(84=2^2\times3\times7\) और \(10=2\times5\), इसलिए \(840=2^3\times3\times5\times7\)। / \(84=2^2\times3\times7\) and \(10=2\times5\), so \(840=2^3\times3\times5\times7\).
Step 3
Exam Tip
तुलना करने पर (a=3) है। / Comparing gives (a=3).
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यदि \(945=3^b\times5\times7\), तो (b) का मान क्या है?
If \(945=3^b\times5\times7\), what is the value of (b)?
#exponent-comparison
#prime-factorisation
#medium
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
\(945=27\times35\) है। / \(945=27\times35\).
Step 2
Why this answer is correct
\(27=3^3\) और \(35=5\times7\), इसलिए \(945=3^3\times5\times7\)। / \(27=3^3\) and \(35=5\times7\), so \(945=3^3\times5\times7\).
Step 3
Exam Tip
तुलना करने पर (b=3) मिलेगा। / Comparing gives (b=3).
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यदि \(1225=5^m\times7^2\), तो (m) का मान क्या है?
If \(1225=5^m\times7^2\), what is the value of (m)?
#exponent-comparison
#square-number
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
\(1225=35^2\) है। / \(1225=35^2\).
Step 2
Why this answer is correct
\(35=5\times7\), इसलिए \(1225=5^2\times7^2\)। / Since \(35=5\times7\), \(1225=5^2\times7^2\).
Step 3
Exam Tip
दिए गए रूप से तुलना करने पर (m=2) है। / Comparing with the given form gives (m=2).
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यदि \(1800=2^p\times3^2\times5^2\), तो (p) का मान क्या है?
If \(1800=2^p\times3^2\times5^2\), what is the value of (p)?
#exponent-comparison
#number-1800
#medium
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
\(1800=18\times100\) लिखें। / Write \(1800=18\times100\).
Step 2
Why this answer is correct
\(18=2\times3^2\) और \(100=2^2\times5^2\), इसलिए 2 की कुल घात 3 है। / \(18=2\times3^2\) and \(100=2^2\times5^2\), so the total power of 2 is 3.
Step 3
Exam Tip
इसलिए (p=3) होगा। / Therefore, (p=3).
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times3^2\times7\) है?
Which number has prime factorisation \(2^3\times3^2\times7\)?
#evaluate-factorisation
#number-504
#medium
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? Hint Small clue
A 504
B 252
C 1008
D 756
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
\(8\times9\times7=504\)। / \(8\times9\times7=504\).
Step 3
Exam Tip
अभाज्य घातों का मान पहले निकालें, फिर गुणा करें। / Evaluate prime powers first, then multiply.
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किस संख्या का अभाज्य गुणनखंडन \(2^4\times3\times11\) है?
Which number has prime factorisation \(2^4\times3\times11\)?
#evaluate-factorisation
#number-528
#medium
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+10 Time+ 10 sec extra
? Hint Small clue
A 528
B 264
C 1056
D 396
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) निकालें। / Calculate \(2^4=16\).
Step 2
Why this answer is correct
\(16\times3\times11=528\)। / \(16\times3\times11=528\).
Step 3
Exam Tip
गुणन करते समय पहले छोटे गुणन को पूरा करें। / While multiplying, complete smaller products first.
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किस संख्या का अभाज्य गुणनखंडन \(2^2\times5\times7^2\) है?
Which number has prime factorisation \(2^2\times5\times7^2\)?
#evaluate-factorisation
#number-980
#medium
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? Hint Small clue
A 980
B 490
C 1960
D 700
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\) और \(7^2=49\) निकालें। / Calculate \(2^2=4\) and \(7^2=49\).
Step 2
Why this answer is correct
\(4\times5\times49=980\)। / \(4\times5\times49=980\).
Step 3
Exam Tip
घातों का मान पहले निकालने से गलती कम होती है। / Finding powers first reduces mistakes.
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किस संख्या का अभाज्य गुणनखंडन \(2^6\times3^3\) है?
Which number has prime factorisation \(2^6\times3^3\)?
#evaluate-factorisation
#number-1728
#medium
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? Hint Small clue
A 1728
B 864
C 3456
D 1296
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\) और \(3^3=27\) निकालें। / Calculate \(2^6=64\) and \(3^3=27\).
Step 2
Why this answer is correct
\(64\times27=1728\)। / \(64\times27=1728\).
Step 3
Exam Tip
बड़ी घातों को पहले अलग से सरल करें। / Simplify higher powers separately first.
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किस संख्या का अभाज्य गुणनखंडन \(2^2\times3^2\times5\times11\) है?
Which number has prime factorisation \(2^2\times3^2\times5\times11\)?
#evaluate-factorisation
#number-1980
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 1980
B 990
C 3960
D 1080
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
\(4\times9\times5\times11=1980\)। / \(4\times9\times5\times11=1980\).
Step 3
Exam Tip
घातों को पहले सरल करने से उत्तर जल्दी मिलता है। / Simplifying powers first gives the answer quickly.
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यदि \(n=2^5\times3\times7\), तो (n) का मान क्या है?
If \(n=2^5\times3\times7\), what is the value of (n)?
#evaluate-factorisation
#powers
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 672
B 336
C 1008
D 504
Explanation opens after your attempt
Step 1
Concept
\(2^5=32\) है। / \(2^5=32\).
Step 2
Why this answer is correct
\(32\times3\times7=672\)। / \(32\times3\times7=672\).
Step 3
Exam Tip
अभाज्य गुणनखंडन को संख्या में बदलने के लिए सभी गुणनखंडों का गुणा करें। / Multiply all factors to convert prime factorisation into the number.
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यदि \(m=3^3\times5\times7\), तो (m) का मान क्या है?
If \(m=3^3\times5\times7\), what is the value of (m)?
#evaluate-factorisation
#powers
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 945
B 315
C 1890
D 735
Explanation opens after your attempt
Step 1
Concept
\(3^3=27\) है। / \(3^3=27\).
Step 2
Why this answer is correct
\(27\times5\times7=945\)। / \(27\times5\times7=945\).
Step 3
Exam Tip
घात वाले भाग को पहले सरल करना ठीक रहता है। / It is better to simplify the power part first.
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किस विकल्प में केवल अभाज्य गुणनखंड दिए गए हैं?
Which option contains only prime factors?
#prime-factors
#concept-check
#medium
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? Hint Small clue
A \(2^3\times3^2\times5\times7\)
B \(8\times9\times5\times7\)
C \(2^3\times9\times35\)
D \(4\times3^2\times5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times7\)
Step 1
Concept
अभाज्य गुणनखंडन में आधार अभाज्य होने चाहिए। / In prime factorisation, bases 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, 9, 35 और 4 संयुक्त हैं, इसलिए बाकी रूप अंतिम नहीं हैं। / 8, 9, 35, and 4 are composite, so the other forms are not final.
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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
#medium
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? Hint Small clue
A \(2^3\times21\times5\)
B \(2^3\times3\times5\times7\)
C \(2^2\times3^2\times7\)
D \(3^3\times5\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times21\times5\)
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
21 संयुक्त संख्या है, इसलिए \(2^3\times21\times5\) अंतिम रूप नहीं है। / 21 is composite, so \(2^3\times21\times5\) is not final form.
Step 3
Exam Tip
21 को \(3\times7\) में बदलें। / Change 21 into \(3\times7\).
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संख्या 2048 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 2048?
#prime-factorisation
#power-of-two
#medium
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^{11}\)
B \(2^{10}\)
C \(4^5\times2\)
D \(32\times64\)
Explanation opens after your attempt
Correct Answer
A. \(2^{11}\)
Step 1
Concept
2048 को बार-बार 2 से भाग दें। / Divide 2048 repeatedly by 2.
Step 2
Why this answer is correct
ग्यारह बार 2 मिलने से \(2048=2^{11}\) होता है। / Eleven factors of 2 give \(2048=2^{11}\).
Step 3
Exam Tip
4, 32 और 64 संयुक्त हैं, इसलिए अंतिम रूप में \(2^{11}\) लिखें। / 4, 32, and 64 are composite, so write \(2^{11}\) in final form.
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संख्या 729 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 729?
#prime-factorisation
#power-of-three
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(3^6\)
B \(3^5\)
C \(9^3\)
D \(27^2\)
Explanation opens after your attempt
Correct Answer
A. \(3^6\)
Step 1
Concept
729 को 3 से बार-बार भाग दें। / Divide 729 repeatedly by 3.
Step 2
Why this answer is correct
छह बार 3 मिलने से \(729=3^6\)। / Six factors of 3 give \(729=3^6\).
Step 3
Exam Tip
9 और 27 संयुक्त हैं, इसलिए अंतिम रूप में 3 की घात लिखें। / 9 and 27 are composite, so write a power of 3 in final form.
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संख्या 1331 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1331?
#prime-factorisation
#cube-number
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A \(11^3\)
B \(11^2\)
C \(121\times11\)
D \(1331\times1\)
Explanation opens after your attempt
Correct Answer
A. \(11^3\)
Step 1
Concept
\(1331=11\times121\) लिखें। / Write \(1331=11\times121\).
Step 2
Why this answer is correct
\(121=11^2\), इसलिए \(1331=11^3\)। / \(121=11^2\), so \(1331=11^3\).
Step 3
Exam Tip
121 संयुक्त है, इसलिए अंतिम रूप में \(11^3\) लिखें। / Since 121 is composite, write \(11^3\) in the final form.
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संख्या 2401 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2401?
#prime-factorisation
#power-of-seven
#medium
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+10 Time+ 10 sec extra
? Hint Small clue
A \(7^4\)
B \(7^3\)
C \(49^2\)
D \(7\times343\)
Explanation opens after your attempt
Correct Answer
A. \(7^4\)
Step 1
Concept
\(2401=49\times49\) लिखा जा सकता है। / (2401) can be written as \(49\times49\).
Step 2
Why this answer is correct
\(49=7^2\), इसलिए \(2401=7^4\)। / Since \(49=7^2\), \(2401=7^4\).
Step 3
Exam Tip
49 संयुक्त है, इसलिए अंतिम अभाज्य रूप में 7 की घात लिखें। / Since 49 is composite, write the power of 7 in final prime form.
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संख्या 2500 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 2500?
#prime-factorisation
#number-2500
#medium
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? Hint Small clue
A \(2^2\times5^4\)
B \(2^4\times5^2\)
C \(25\times100\)
D \(50\times50\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times5^4\)
Step 1
Concept
\(2500=25\times100\) लिखें। / Write \(2500=25\times100\).
Step 2
Why this answer is correct
\(25=5^2\) और \(100=2^2\times5^2\), इसलिए \(2500=2^2\times5^4\)। / \(25=5^2\) and \(100=2^2\times5^2\), so \(2500=2^2\times5^4\).
Step 3
Exam Tip
5 की कुल घात 4 गिनें। / Count the total power of 5 as 4.
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संख्या 2744 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2744?
#prime-factorisation
#cube-number
#medium
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+10 Time+ 10 sec extra
? Hint Small clue
A \(2^3\times7^3\)
B \(14^3\)
C \(2^2\times7^4\)
D \(8\times343\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times7^3\)
Step 1
Concept
\(2744=14^3\) पहचाना जा सकता है। / Recognise \(2744=14^3\).
Step 2
Why this answer is correct
\(14=2\times7\), इसलिए \(2744=2^3\times7^3\)। / Since \(14=2\times7\), \(2744=2^3\times7^3\).
Step 3
Exam Tip
14 संयुक्त है, इसलिए अंतिम रूप में अभाज्य आधार लिखें। / Since 14 is composite, write prime bases in final form.
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यदि \(2^4\times3^2\times5\) से संख्या बनाई जाए, तो वह कौन सी होगी?
If a number is formed from \(2^4\times3^2\times5\), which number will it be?
#evaluate-factorisation
#mcq-pattern
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 720
B 360
C 1440
D 1080
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
\(16\times9\times5=720\)। / \(16\times9\times5=720\).
Step 3
Exam Tip
घातों को पहले हल करने से विकल्प जल्दी मिल जाता है। / Solving powers first helps find the option quickly.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^3\times3^2\times5^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^3\times3^2\times5^2\), which number is it?
#evaluate-factorisation
#number-1800
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 1800
B 900
C 3600
D 1200
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\), \(3^2=9\) और \(5^2=25\) निकालें। / Calculate \(2^3=8\), \(3^2=9\), and \(5^2=25\).
Step 2
Why this answer is correct
\(8\times9\times25=1800\)। / \(8\times9\times25=1800\).
Step 3
Exam Tip
तीनों घातों का मान अलग-अलग निकालकर गुणा करें। / Find each power separately and then multiply.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4\times3^4\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^4\times3^4\), which number is it?
#evaluate-factorisation
#number-1296
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 1296
B 648
C 2592
D 1728
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(3^4=81\) हैं। / \(2^4=16\) and \(3^4=81\).
Step 2
Why this answer is correct
\(16\times81=1296\)। / \(16\times81=1296\).
Step 3
Exam Tip
ऐसी गणना में घातों को पहले सरल करना सुरक्षित रहता है। / In such calculations, simplifying powers first is safer.
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यदि \(2^2\times5^4\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^2\times5^4\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#number-2500
#medium
50 50-50 2 wrong hide
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+10 Time+ 10 sec extra
? Hint Small clue
A 2500
B 1250
C 5000
D 625
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\) और \(5^4=625\) निकालें। / Calculate \(2^2=4\) and \(5^4=625\).
Step 2
Why this answer is correct
\(4\times625=2500\)। / \(4\times625=2500\).
Step 3
Exam Tip
बड़ी घात को पहले निकालने से उत्तर आसान बनता है। / Finding the higher power first makes the answer easier.
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संख्या 2700 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2700?
#prime-factorisation
#number-2700
#medium
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^2\times3^3\times5^2\)
B \(2\times3^3\times5^2\)
C \(27\times100\)
D \(2^2\times3^2\times5^3\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\times5^2\)
Step 1
Concept
\(2700=27\times100\) लिखें। / Write \(2700=27\times100\).
Step 2
Why this answer is correct
\(27=3^3\) और \(100=2^2\times5^2\), इसलिए \(2700=2^2\times3^3\times5^2\)। / \(27=3^3\) and \(100=2^2\times5^2\), so \(2700=2^2\times3^3\times5^2\).
Step 3
Exam Tip
27 और 100 दोनों को अभाज्य घातों में बदलें। / Convert both 27 and 100 into prime powers.
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संख्या 3080 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 3080?
#prime-factorisation
#number-3080
#medium
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^3\times5\times7\times11\)
B \(2^2\times5\times7\times11\)
C \(28\times110\)
D \(8\times385\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times5\times7\times11\)
Step 1
Concept
\(3080=8\times385\) लिखें। / Write \(3080=8\times385\).
Step 2
Why this answer is correct
\(8=2^3\) और \(385=5\times7\times11\), इसलिए \(3080=2^3\times5\times7\times11\)। / \(8=2^3\) and \(385=5\times7\times11\), so \(3080=2^3\times5\times7\times11\).
Step 3
Exam Tip
385 को भी अभाज्य रूप में तोड़ें। / Break 385 into prime form too.
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संख्या 3960 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 3960?
#prime-factorisation
#number-3960
#medium
50 50-50 2 wrong hide
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? Hint Small clue
A \(2^3\times3^2\times5\times11\)
B \(2^2\times3^2\times5\times11\)
C \(36\times110\)
D \(2^3\times9\times55\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5\times11\)
Step 1
Concept
\(3960=36\times110\) लिखें। / Write \(3960=36\times110\).
Step 2
Why this answer is correct
\(36=2^2\times3^2\) और \(110=2\times5\times11\), इसलिए \(3960=2^3\times3^2\times5\times11\)। / \(36=2^2\times3^2\) and \(110=2\times5\times11\), so \(3960=2^3\times3^2\times5\times11\).
Step 3
Exam Tip
2 की कुल घात ध्यान से गिनें। / Count the total power of 2 carefully.
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times5\times7\times11\) है?
Which number has prime factorisation \(2^3\times5\times7\times11\)?
#evaluate-factorisation
#number-3080
#medium
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? Hint Small clue
A 3080
B 1540
C 6160
D 3850
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) निकालें। / Calculate \(2^3=8\).
Step 2
Why this answer is correct
\(8\times5\times7\times11=3080\)। / \(8\times5\times7\times11=3080\).
Step 3
Exam Tip
क्रम कोई भी हो, गुणनफल वही रहेगा। / Whatever the order, the product remains the same.
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संख्या 4096 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 4096?
#prime-factorisation
#power-of-two
#medium
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A \(2^{12}\)
B \(2^{11}\)
C \(64^2\)
D \(16^3\)
Explanation opens after your attempt
Correct Answer
A. \(2^{12}\)
Step 1
Concept
4096 को बार-बार 2 से भाग दें। / Divide 4096 repeatedly by 2.
Step 2
Why this answer is correct
बारह बार 2 मिलने से \(4096=2^{12}\) होता है। / Twelve factors of 2 give \(4096=2^{12}\).
Step 3
Exam Tip
64 और 16 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप नहीं हैं। / 64 and 16 are composite, so they are not final prime forms.
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अभाज्य गुणनखंडन में \(12^2\) को अंतिम रूप क्यों नहीं माना जाता?
Why is \(12^2\) not considered a final form in prime factorisation?
#prime-factorisation
#concept-check
#medium
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A क्योंकि 12 संयुक्त संख्या है / Because 12 is composite
B क्योंकि 12 अभाज्य संख्या है / Because 12 is prime
C क्योंकि वर्ग संख्या का गुणनखंडन नहीं होता / Because square numbers cannot be factorised
D क्योंकि घात लिखना गलत है / Because writing powers is wrong
Explanation opens after your attempt
Correct Answer
A. क्योंकि 12 संयुक्त संख्या है / Because 12 is composite
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में आधार अभाज्य होना चाहिए। / In final prime factorisation, the base must be prime.
Step 2
Why this answer is correct
12 संयुक्त है और \(12=2^2\times3\) है। / 12 is composite and \(12=2^2\times3\).
Step 3
Exam Tip
इसलिए \(12^2\) को आगे \(2^4\times3^2\) में बदलना होगा। / Therefore, \(12^2\) must be changed further into \(2^4\times3^2\).
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