अंतिम अभाज्य गुणनखंडन में संयुक्त आधार बच जाने पर उत्तर अधूरा क्यों माना जाता है?
Why is the answer considered incomplete if a composite base remains in final prime factorisation?
#prime-factorisation
#final-form
#expert
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A क्योंकि अंतिम रूप में केवल अभाज्य आधार रहने चाहिए / Because only prime bases should remain in the final form
B क्योंकि घात का प्रयोग गलत हो जाता है / Because using powers becomes wrong
C क्योंकि संख्या का मान हमेशा बदल जाता है / Because the value of the number always changes
D क्योंकि गुणन की जगह जोड़ करना चाहिए / Because addition should be used instead of multiplication
Explanation opens after your attempt
Correct Answer
A. क्योंकि अंतिम रूप में केवल अभाज्य आधार रहने चाहिए / Because only prime bases should remain in the final form
Step 1
Concept
अभाज्य गुणनखंडन का उद्देश्य संख्या को केवल अभाज्य आधारों में लिखना है। / The aim of prime factorisation is to write the number using prime bases only.
Step 2
Why this answer is correct
यदि (45) या (121) जैसा आधार बचा है, तो वह संयुक्त है और आगे टूटेगा। / If a base like (45) or (121) remains, it is composite and must be broken further.
Step 3
Exam Tip
अंतिम उत्तर लिखने से पहले हर आधार की अभाज्यता जांचें। / Before writing the final answer, check whether every base is prime.
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संख्या 680400 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 680400?
#prime-factorisation
#number-680400
#expert
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A \(2^4\times3^5\times5^2\times7\)
B \(2^5\times3^4\times5^2\times7\)
C \(16\times42525\)
D \(2^4\times243\times25\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^5\times5^2\times7\)
Step 1
Concept
\(680400=16\times42525\) लिखें। / Write \(680400=16\times42525\).
Step 2
Why this answer is correct
\(16=2^4\) और \(42525=3^5\times5^2\times7\), इसलिए सही रूप \(2^4\times3^5\times5^2\times7\) है। / \(16=2^4\) and \(42525=3^5\times5^2\times7\), so the correct form is \(2^4\times3^5\times5^2\times7\).
Step 3
Exam Tip
42525 को अंतिम रूप में न छोड़ें। / Do not leave 42525 in the final form.
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संख्या 627264 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 627264?
#prime-factorisation
#number-627264
#expert
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A \(2^6\times3^4\times11^2\)
B \(2^5\times3^5\times11^2\)
C \(64\times9801\)
D \(2^6\times81\times121\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^4\times11^2\)
Step 1
Concept
\(627264=64\times9801\) लिखें। / Write \(627264=64\times9801\).
Step 2
Why this answer is correct
\(64=2^6\) और \(9801=3^4\times11^2\), इसलिए \(627264=2^6\times3^4\times11^2\)। / \(64=2^6\) and \(9801=3^4\times11^2\), so \(627264=2^6\times3^4\times11^2\).
Step 3
Exam Tip
9801 को अभाज्य घातों में बदलें। / Convert 9801 into prime powers.
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संख्या 379080 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 379080?
#prime-factorisation
#number-379080
#expert
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A \(2^3\times3^6\times5\times13\)
B \(2^4\times3^5\times5\times13\)
C \(8\times47385\)
D \(2^3\times729\times65\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^6\times5\times13\)
Step 1
Concept
\(379080=8\times47385\) लिखें। / Write \(379080=8\times47385\).
Step 2
Why this answer is correct
\(8=2^3\) और \(47385=3^6\times5\times13\), इसलिए सही रूप \(2^3\times3^6\times5\times13\) है। / \(8=2^3\) and \(47385=3^6\times5\times13\), so the correct form is \(2^3\times3^6\times5\times13\).
Step 3
Exam Tip
47385 को पूरी तरह अभाज्य रूप दें। / Give 47385 its complete prime form.
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संख्या 196000 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 196000?
#prime-factorisation
#number-196000
#expert
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A \(2^5\times5^3\times7^2\)
B \(2^4\times5^4\times7\)
C \(32\times6125\)
D \(2^5\times125\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times5^3\times7^2\)
Step 1
Concept
\(196000=32\times6125\) लिखें। / Write \(196000=32\times6125\).
Step 2
Why this answer is correct
\(32=2^5\) और \(6125=5^3\times7^2\), इसलिए \(196000=2^5\times5^3\times7^2\)। / \(32=2^5\) and \(6125=5^3\times7^2\), so \(196000=2^5\times5^3\times7^2\).
Step 3
Exam Tip
6125 को अंतिम उत्तर में न रखें। / Do not keep 6125 in the final answer.
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संख्या 289575 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 289575?
#prime-factorisation
#number-289575
#expert
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A \(3^4\times5^2\times11\times13\)
B \(3^5\times5\times11\times13\)
C \(81\times3575\)
D \(3^4\times25\times143\)
Explanation opens after your attempt
Correct Answer
A. \(3^4\times5^2\times11\times13\)
Step 1
Concept
\(289575=81\times3575\) लिखें। / Write \(289575=81\times3575\).
Step 2
Why this answer is correct
\(81=3^4\) और \(3575=5^2\times11\times13\), इसलिए \(289575=3^4\times5^2\times11\times13\)। / \(81=3^4\) and \(3575=5^2\times11\times13\), so \(289575=3^4\times5^2\times11\times13\).
Step 3
Exam Tip
3575 को भी पूरा अभाज्य रूप दें। / Give 3575 its complete prime form too.
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संख्या 177408 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 177408?
#prime-factorisation
#number-177408
#expert
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A \(2^8\times3^2\times7\times11\)
B \(2^7\times3^3\times7\times11\)
C \(256\times693\)
D \(2^8\times9\times77\)
Explanation opens after your attempt
Correct Answer
A. \(2^8\times3^2\times7\times11\)
Step 1
Concept
\(177408=256\times693\) लिखें। / Write \(177408=256\times693\).
Step 2
Why this answer is correct
\(256=2^8\) और \(693=3^2\times7\times11\), इसलिए सही रूप \(2^8\times3^2\times7\times11\) है। / \(256=2^8\) and \(693=3^2\times7\times11\), so the correct form is \(2^8\times3^2\times7\times11\).
Step 3
Exam Tip
693 को अभाज्य रूप में बदलें। / Convert 693 into prime form.
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संख्या 529200 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 529200?
#prime-factorisation
#number-529200
#expert
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A \(2^4\times3^3\times5^2\times7^2\)
B \(2^5\times3^2\times5^2\times7^2\)
C \(16\times33075\)
D \(2^4\times27\times25\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^3\times5^2\times7^2\)
Step 1
Concept
\(529200=16\times33075\) लिखें। / Write \(529200=16\times33075\).
Step 2
Why this answer is correct
\(33075=3^3\times5^2\times7^2\), इसलिए \(529200=2^4\times3^3\times5^2\times7^2\)। / \(33075=3^3\times5^2\times7^2\), so \(529200=2^4\times3^3\times5^2\times7^2\).
Step 3
Exam Tip
33075 को अंतिम रूप में न छोड़ें। / Do not leave 33075 in the final form.
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संख्या 155520 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 155520?
#prime-factorisation
#number-155520
#expert
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A \(2^7\times3^5\times5\)
B \(2^6\times3^5\times5\)
C \(128\times1215\)
D \(2^7\times243\times5\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^5\times5\)
Step 1
Concept
\(155520=128\times1215\) लिखें। / Write \(155520=128\times1215\).
Step 2
Why this answer is correct
\(128=2^7\) और \(1215=3^5\times5\), इसलिए \(155520=2^7\times3^5\times5\)। / \(128=2^7\) and \(1215=3^5\times5\), so \(155520=2^7\times3^5\times5\).
Step 3
Exam Tip
1215 को अभाज्य घातों में बदलें। / Convert 1215 into prime powers.
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संख्या 174636 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 174636?
#prime-factorisation
#number-174636
#expert
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A \(2^2\times3^4\times7^2\times11\)
B \(2^3\times3^3\times7^2\times11\)
C \(4\times43659\)
D \(2^2\times81\times49\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^4\times7^2\times11\)
Step 1
Concept
\(174636=4\times43659\) लिखें। / Write \(174636=4\times43659\).
Step 2
Why this answer is correct
\(4=2^2\) और \(43659=3^4\times7^2\times11\), इसलिए सही रूप \(2^2\times3^4\times7^2\times11\) है। / \(4=2^2\) and \(43659=3^4\times7^2\times11\), so the correct form is \(2^2\times3^4\times7^2\times11\).
Step 3
Exam Tip
43659 को अभाज्य घातों में बदलें। / Convert 43659 into prime powers.
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संख्या 79200 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 79200?
#prime-factorisation
#number-79200
#expert
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A \(2^5\times3^2\times5^2\times11\)
B \(2^4\times3^3\times5^2\times11\)
C \(32\times2475\)
D \(2^5\times9\times25\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^2\times5^2\times11\)
Step 1
Concept
\(79200=32\times2475\) लिखें। / Write \(79200=32\times2475\).
Step 2
Why this answer is correct
\(2475=3^2\times5^2\times11\), इसलिए \(79200=2^5\times3^2\times5^2\times11\)। / \(2475=3^2\times5^2\times11\), so \(79200=2^5\times3^2\times5^2\times11\).
Step 3
Exam Tip
2475 को पूरा अभाज्य रूप दें। / Give 2475 its complete prime form.
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संख्या 415800 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 415800?
#prime-factorisation
#number-415800
#expert
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A \(2^3\times3^3\times5^2\times7\times11\)
B \(2^4\times3^2\times5^2\times7\times11\)
C \(8\times51975\)
D \(2^3\times27\times25\times77\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times5^2\times7\times11\)
Step 1
Concept
\(415800=8\times51975\) लिखें। / Write \(415800=8\times51975\).
Step 2
Why this answer is correct
\(51975=3^3\times5^2\times7\times11\), इसलिए \(415800=2^3\times3^3\times5^2\times7\times11\)। / \(51975=3^3\times5^2\times7\times11\), so \(415800=2^3\times3^3\times5^2\times7\times11\).
Step 3
Exam Tip
51975 को अंतिम रूप में न छोड़ें। / Do not leave 51975 in the final form.
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संख्या 762048 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 762048?
#prime-factorisation
#number-762048
#expert
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A \(2^6\times3^5\times7^2\)
B \(2^5\times3^6\times7^2\)
C \(64\times11907\)
D \(2^6\times243\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^5\times7^2\)
Step 1
Concept
\(762048=64\times11907\) लिखें। / Write \(762048=64\times11907\).
Step 2
Why this answer is correct
\(64=2^6\) और \(11907=3^5\times7^2\), इसलिए \(762048=2^6\times3^5\times7^2\)। / \(64=2^6\) and \(11907=3^5\times7^2\), so \(762048=2^6\times3^5\times7^2\).
Step 3
Exam Tip
11907 को अभाज्य घातों में लिखें। / Write 11907 as prime powers.
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संख्या 137200 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 137200?
#prime-factorisation
#number-137200
#expert
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A \(2^4\times5^2\times7^3\)
B \(2^3\times5^3\times7^2\)
C \(16\times8575\)
D \(2^4\times25\times343\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times5^2\times7^3\)
Step 1
Concept
\(137200=16\times8575\) लिखें। / Write \(137200=16\times8575\).
Step 2
Why this answer is correct
\(16=2^4\) और \(8575=5^2\times7^3\), इसलिए सही रूप \(2^4\times5^2\times7^3\) है। / \(16=2^4\) and \(8575=5^2\times7^3\), so the correct form is \(2^4\times5^2\times7^3\).
Step 3
Exam Tip
8575 को अंतिम अभाज्य रूप दें। / Give 8575 its final prime form.
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संख्या 127575 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 127575?
#prime-factorisation
#number-127575
#expert
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A \(3^6\times5^2\times7\)
B \(3^5\times5^3\times7\)
C \(729\times175\)
D \(3^6\times25\times7\)
Explanation opens after your attempt
Correct Answer
A. \(3^6\times5^2\times7\)
Step 1
Concept
\(127575=729\times175\) लिखें। / Write \(127575=729\times175\).
Step 2
Why this answer is correct
\(729=3^6\) और \(175=5^2\times7\), इसलिए \(127575=3^6\times5^2\times7\)। / \(729=3^6\) and \(175=5^2\times7\), so \(127575=3^6\times5^2\times7\).
Step 3
Exam Tip
729 और 175 दोनों को अभाज्य रूप दें। / Give prime form to both 729 and 175.
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संख्या 453600 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 453600?
#prime-factorisation
#number-453600
#expert
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A \(2^5\times3^4\times5^2\times7\)
B \(2^4\times3^5\times5^2\times7\)
C \(32\times14175\)
D \(2^5\times81\times25\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^4\times5^2\times7\)
Step 1
Concept
\(453600=32\times14175\) लिखें। / Write \(453600=32\times14175\).
Step 2
Why this answer is correct
\(14175=3^4\times5^2\times7\), इसलिए \(453600=2^5\times3^4\times5^2\times7\)। / \(14175=3^4\times5^2\times7\), so \(453600=2^5\times3^4\times5^2\times7\).
Step 3
Exam Tip
14175 को अंतिम रूप में न छोड़ें। / Do not leave 14175 in the final form.
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संख्या 139392 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 139392?
#prime-factorisation
#number-139392
#expert
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A \(2^7\times3^2\times11^2\)
B \(2^6\times3^3\times11^2\)
C \(128\times1089\)
D \(2^7\times9\times121\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^2\times11^2\)
Step 1
Concept
\(139392=128\times1089\) लिखें। / Write \(139392=128\times1089\).
Step 2
Why this answer is correct
\(128=2^7\) और \(1089=3^2\times11^2\), इसलिए \(139392=2^7\times3^2\times11^2\)। / \(128=2^7\) and \(1089=3^2\times11^2\), so \(139392=2^7\times3^2\times11^2\).
Step 3
Exam Tip
1089 को अभाज्य घातों में बदलें। / Convert 1089 into prime powers.
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संख्या 117000 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 117000?
#prime-factorisation
#number-117000
#expert
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A \(2^3\times3^2\times5^3\times13\)
B \(2^2\times3^3\times5^3\times13\)
C \(8\times14625\)
D \(2^3\times9\times125\times13\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\times5^3\times13\)
Step 1
Concept
\(117000=8\times14625\) लिखें। / Write \(117000=8\times14625\).
Step 2
Why this answer is correct
\(14625=3^2\times5^3\times13\), इसलिए \(117000=2^3\times3^2\times5^3\times13\)। / \(14625=3^2\times5^3\times13\), so \(117000=2^3\times3^2\times5^3\times13\).
Step 3
Exam Tip
14625 को पूरा अभाज्य रूप दें। / Give 14625 its complete prime form.
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संख्या 475200 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 475200?
#prime-factorisation
#number-475200
#expert
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? Hint Small clue
A \(2^6\times3^3\times5^2\times11\)
B \(2^5\times3^4\times5^2\times11\)
C \(64\times7425\)
D \(2^6\times27\times25\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^3\times5^2\times11\)
Step 1
Concept
\(475200=64\times7425\) लिखें। / Write \(475200=64\times7425\).
Step 2
Why this answer is correct
\(7425=3^3\times5^2\times11\), इसलिए \(475200=2^6\times3^3\times5^2\times11\)। / \(7425=3^3\times5^2\times11\), so \(475200=2^6\times3^3\times5^2\times11\).
Step 3
Exam Tip
7425 को अंतिम रूप में न छोड़ें। / Do not leave 7425 in the final form.
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संख्या 99225 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 99225?
#prime-factorisation
#number-99225
#expert
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A \(3^4\times5^2\times7^2\)
B \(3^3\times5^3\times7^2\)
C \(81\times1225\)
D \(9\times11025\)
Explanation opens after your attempt
Correct Answer
A. \(3^4\times5^2\times7^2\)
Step 1
Concept
\(99225=81\times1225\) लिखें। / Write \(99225=81\times1225\).
Step 2
Why this answer is correct
\(81=3^4\) और \(1225=5^2\times7^2\), इसलिए \(99225=3^4\times5^2\times7^2\)। / \(81=3^4\) and \(1225=5^2\times7^2\), so \(99225=3^4\times5^2\times7^2\).
Step 3
Exam Tip
1225 को अभाज्य घातों में बदलें। / Convert 1225 into prime powers.
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संख्या 518400 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 518400?
#prime-factorisation
#number-518400
#expert
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A \(2^8\times3^4\times5^2\)
B \(2^7\times3^5\times5^2\)
C \(256\times2025\)
D \(2^8\times81\times25\)
Explanation opens after your attempt
Correct Answer
A. \(2^8\times3^4\times5^2\)
Step 1
Concept
\(518400=256\times2025\) लिखें। / Write \(518400=256\times2025\).
Step 2
Why this answer is correct
\(256=2^8\) और \(2025=3^4\times5^2\), इसलिए \(518400=2^8\times3^4\times5^2\)। / \(256=2^8\) and \(2025=3^4\times5^2\), so \(518400=2^8\times3^4\times5^2\).
Step 3
Exam Tip
2025 को अंतिम अभाज्य रूप दें। / Give 2025 its final prime form.
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यदि \(529200=2^4\times3^3\times5^2\times7^q\), तो (q) का मान क्या है?
If \(529200=2^4\times3^3\times5^2\times7^q\), what is the value of (q)?
#exponent-comparison
#number-529200
#expert
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A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
\(529200=16\times33075\) है। / \(529200=16\times33075\).
Step 2
Why this answer is correct
\(33075=3^3\times5^2\times7^2\), इसलिए 7 की घात 2 है। / \(33075=3^3\times5^2\times7^2\), so the power of 7 is 2.
Step 3
Exam Tip
तुलना करने पर (q=2) मिलता है। / Comparing gives (q=2).
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यदि \(627264=2^a\times3^4\times11^2\), तो (a) का मान क्या है?
If \(627264=2^a\times3^4\times11^2\), what is the value of (a)?
#exponent-comparison
#number-627264
#expert
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A 6
B 5
C 7
D 4
Explanation opens after your attempt
Step 1
Concept
\(627264=64\times9801\) लिखें। / Write \(627264=64\times9801\).
Step 2
Why this answer is correct
\(64=2^6\) और \(9801=3^4\times11^2\), इसलिए 2 की घात 6 है। / \(64=2^6\) and \(9801=3^4\times11^2\), so the power of 2 is 6.
Step 3
Exam Tip
दिए गए रूप से (a=6) है। / From the given form, (a=6).
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यदि \(680400=2^4\times3^b\times5^2\times7\), तो (b) का मान क्या है?
If \(680400=2^4\times3^b\times5^2\times7\), what is the value of (b)?
#exponent-comparison
#number-680400
#expert
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A 5
B 4
C 6
D 3
Explanation opens after your attempt
Step 1
Concept
\(680400=16\times42525\) है। / \(680400=16\times42525\).
Step 2
Why this answer is correct
\(42525=3^5\times5^2\times7\), इसलिए 3 की घात 5 है। / \(42525=3^5\times5^2\times7\), so the power of 3 is 5.
Step 3
Exam Tip
तुलना करने पर (b=5) होगा। / Comparing gives (b=5).
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यदि \(137200=2^4\times5^2\times7^p\), तो (p) का मान क्या है?
If \(137200=2^4\times5^2\times7^p\), what is the value of (p)?
#exponent-comparison
#number-137200
#expert
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A 3
B 2
C 4
D 1
Explanation opens after your attempt
Step 1
Concept
\(137200=16\times8575\) लिखें। / Write \(137200=16\times8575\).
Step 2
Why this answer is correct
\(8575=5^2\times7^3\), इसलिए 7 की घात 3 है। / \(8575=5^2\times7^3\), so the power of 7 is 3.
Step 3
Exam Tip
दिए गए रूप से (p=3) मिलेगा। / From the given form, (p=3).
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किस संख्या का अभाज्य गुणनखंडन \(2^6\times3^5\times7^2\) है?
Which number has prime factorisation \(2^6\times3^5\times7^2\)?
#evaluate-factorisation
#number-762048
#expert
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A 762048
B 381024
C 1524096
D 190512
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\), \(3^5=243\) और \(7^2=49\) निकालें। / Calculate \(2^6=64\), \(3^5=243\), and \(7^2=49\).
Step 2
Why this answer is correct
\(64\times243\times49=762048\)। / \(64\times243\times49=762048\).
Step 3
Exam Tip
ऐसी गणना में घातों को पहले हल करें। / In such calculations, solve powers first.
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किस संख्या का अभाज्य गुणनखंडन \(2^4\times3^5\times7^2\) है?
Which number has prime factorisation \(2^4\times3^5\times7^2\)?
#evaluate-factorisation
#number-190512
#expert
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A 190512
B 95256
C 381024
D 127008
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\), \(3^5=243\) और \(7^2=49\) निकालें। / Calculate \(2^4=16\), \(3^5=243\), and \(7^2=49\).
Step 2
Why this answer is correct
\(16\times243\times49=190512\)। / \(16\times243\times49=190512\).
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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किस संख्या का अभाज्य गुणनखंडन \(2^7\times3^2\times11^2\) है?
Which number has prime factorisation \(2^7\times3^2\times11^2\)?
#evaluate-factorisation
#number-139392
#expert
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A 139392
B 69696
C 278784
D 177408
Explanation opens after your attempt
Step 1
Concept
\(2^7=128\), \(3^2=9\) और \(11^2=121\) निकालें। / Calculate \(2^7=128\), \(3^2=9\), and \(11^2=121\).
Step 2
Why this answer is correct
\(128\times9\times121=139392\)। / \(128\times9\times121=139392\).
Step 3
Exam Tip
पहले घातों का मान निकालें, फिर गुणा करें। / Find the values of powers first, then multiply.
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किस संख्या का अभाज्य गुणनखंडन \(3^4\times5^2\times7^2\) है?
Which number has prime factorisation \(3^4\times5^2\times7^2\)?
#evaluate-factorisation
#number-99225
#expert
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A 99225
B 49612
C 198450
D 11025
Explanation opens after your attempt
Step 1
Concept
\(3^4=81\), \(5^2=25\) और \(7^2=49\) निकालें। / Calculate \(3^4=81\), \(5^2=25\), and \(7^2=49\).
Step 2
Why this answer is correct
\(81\times25\times49=99225\)। / \(81\times25\times49=99225\).
Step 3
Exam Tip
वर्ग घातों को जल्दबाजी में न छोड़ें। / Do not skip square powers in a hurry.
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times3^6\times5\times13\) है?
Which number has prime factorisation \(2^3\times3^6\times5\times13\)?
#evaluate-factorisation
#number-379080
#expert
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A 379080
B 189540
C 758160
D 117000
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) और \(3^6=729\) निकालें। / Calculate \(2^3=8\) and \(3^6=729\).
Step 2
Why this answer is correct
\(8\times729\times5\times13=379080\)। / \(8\times729\times5\times13=379080\).
Step 3
Exam Tip
बड़े घात वाले भाग को पहले सरल करें। / Simplify the higher-power part first.
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यदि संख्या \(2^7\times3^4\times5^2\times11^3\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^7\times3^4\times5^2\times11^3\), by which smallest number should it be multiplied to make a perfect square?
#perfect-square
#prime-exponents
#expert
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A 22
B 2
C 11
D 44
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 और 11 की घात 3 विषम हैं। / The powers of 2 and 11 are odd.
Step 3
Exam Tip
\(2\times11=22\) से गुणा करने पर दोनों घातें सम हो जाएंगी। / Multiplying by \(2\times11=22\) makes both powers even.
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यदि संख्या \(2^8\times3^5\times5^4\times7^3\) है, तो इसे पूर्ण वर्ग बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^8\times3^5\times5^4\times7^3\), by which smallest number should it be divided to make a perfect square?
#perfect-square
#division
#expert
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A 21
B 3
C 7
D 63
Explanation opens after your attempt
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
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 भाग देने पर घातें 4 और 2 हो जाएंगी। / Dividing by \(3\times7=21\) makes the powers 4 and 2.
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यदि संख्या \(2^5\times3^4\times5^2\times7^7\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से गुणा करना होगा?
If the number is \(2^5\times3^4\times5^2\times7^7\), by which smallest number should it be multiplied to make a perfect cube?
#perfect-cube
#prime-exponents
#expert
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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 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, 4 को 6, 2 को 3 और 7 को 9 बनाना होगा। / Powers 5, 4, 2, and 7 must become 6, 6, 3, and 9.
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 \(2^{10}\times3^8\times5^5\times11^4\) है, तो इसे पूर्ण घन बनाने के लिए सबसे छोटी किस संख्या से भाग देना होगा?
If the number is \(2^{10}\times3^8\times5^5\times11^4\), by which smallest number should it be divided to make a perfect cube?
#perfect-cube
#division
#expert
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? Hint Small clue
A \(2\times3^2\times5^2\times11\)
B \(2^2\times3\times5\times11\)
C \(2\times3\times5^2\times11^2\)
D \(3^2\times5\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5^2\times11\)
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
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 \(2\times3^2\times5^2\times11\) है। / Therefore, the divisor is \(2\times3^2\times5^2\times11\).
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यदि \(n=2^8\times3^6\times5^2\times7^4\), तो (n) किस संख्या से विभाज्य नहीं होगा?
If \(n=2^8\times3^6\times5^2\times7^4\), by which number will (n) not be divisible?
#divisibility
#prime-exponents
#expert
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A \(5^3\)
B \(2^7\times3^5\)
C \(3^6\times7^3\)
D \(2^8\times5^2\)
Explanation opens after your attempt
Correct Answer
A. \(5^3\)
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 5 की घात 2 है, पर \(5^3\) के लिए घात 3 चाहिए। / (n) has power 2 of 5, but \(5^3\) needs power 3.
Step 3
Exam Tip
इसलिए (n), \(5^3\) से विभाज्य नहीं होगा। / Therefore, (n) is not divisible by \(5^3\).
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यदि \(n=2^9\times3^4\times5^5\times13^2\), तो (n) किस संख्या से अवश्य विभाज्य होगा?
If \(n=2^9\times3^4\times5^5\times13^2\), by which number must (n) be divisible?
#divisibility
#prime-exponents
#expert
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? Hint Small clue
A \(2^8\times3^4\times5^4\times13^2\)
B \(2^{10}\times3^3\)
C \(3^5\times5^2\)
D \(2^9\times13^3\)
Explanation opens after your attempt
Correct Answer
A. \(2^8\times3^4\times5^4\times13^2\)
Step 1
Concept
विभाज्यता के लिए भाजक की घातें संख्या की घातों से अधिक नहीं होनी चाहिए। / For divisibility, the exponents of the divisor must not exceed those in the number.
Step 2
Why this answer is correct
पहले विकल्प में सभी घातें (n) की घातों से कम या बराबर हैं। / In the first option, all exponents are less than or equal to those in (n).
Step 3
Exam Tip
इसलिए (n) उस संख्या से अवश्य विभाज्य होगा। / Therefore, (n) must be divisible by that number.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^8\times3^6\times5^4\times7^3\times11^2\) है, तो दोहराव सहित अभाज्य गुणनखंडों की संख्या कितनी है?
If a number has prime factorisation \(2^8\times3^6\times5^4\times7^3\times11^2\), how many prime factors does it have with repetition?
#counting-prime-factors
#prime-exponents
#expert
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? Hint Small clue
A 23
B 5
C 20
D 25
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
(8+6+4+3+2=23)। / (8+6+4+3+2=23).
Step 3
Exam Tip
केवल आधार गिनना और दोहराव सहित गिनना अलग बातें हैं। / Counting only bases and counting with repetition are different.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^6\times3^5\times5^4\times7^3\times11^2\times13\) है, तो उसमें अलग-अलग अभाज्य गुणनखंड कितने हैं?
If a number has prime factorisation \(2^6\times3^5\times5^4\times7^3\times11^2\times13\), how many distinct prime factors does it have?
#distinct-prime-factors
#prime-exponents
#expert
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? Hint Small clue
A 6
B 21
C 5
D 7
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, 5, 7, 11 और 13 हैं। / The bases are 2, 3, 5, 7, 11, and 13.
Step 3
Exam Tip
इसलिए अलग-अलग अभाज्य गुणनखंडों की संख्या 6 है। / Therefore, the number of distinct prime factors is 6.
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यदि \(a=2^5\times3^3\times5^2\times11\) और \(b=2^4\times3^5\times7\times11^2\), तो (ab) में 11 की घात क्या होगी?
If \(a=2^5\times3^3\times5^2\times11\) and \(b=2^4\times3^5\times7\times11^2\), what will be the power of 11 in (ab)?
#product-factorisation
#powers
#expert
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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 11 की घात 1 है और (b) में 11 की घात 2 है। / The power of 11 in (a) is 1 and in (b) is 2.
Step 3
Exam Tip
(ab) में 11 की घात (1+2=3) होगी। / In (ab), the power of 11 will be (1+2=3).
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यदि \(x=2^6\times3^4\times7^2\) और \(y=2^3\times3^5\times5\times7\), तो (xy) में 3 की घात क्या होगी?
If \(x=2^6\times3^4\times7^2\) and \(y=2^3\times3^5\times5\times7\), what will be the power of 3 in (xy)?
#product-factorisation
#powers
#expert
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A 9
B 5
C 4
D 8
Explanation opens after your attempt
Step 1
Concept
समान आधार 3 की घातें गुणा में जुड़ती हैं। / Powers with the same base 3 are added in multiplication.
Step 2
Why this answer is correct
(x) में 3 की घात 4 है और (y) में 3 की घात 5 है। / The power of 3 in (x) is 4 and in (y) is 5.
Step 3
Exam Tip
कुल घात (4+5=9) होगी। / The total power will be (4+5=9).
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किस विकल्प में \(2^6\times3^4\times11^2\) का सही मान है?
Which option gives the correct value of \(2^6\times3^4\times11^2\)?
#evaluate-factorisation
#number-627264
#expert
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A 627264
B 313632
C 1254528
D 139392
Explanation opens after your attempt
Step 1
Concept
\(2^6=64\), \(3^4=81\) और \(11^2=121\) निकालें। / Calculate \(2^6=64\), \(3^4=81\), and \(11^2=121\).
Step 2
Why this answer is correct
\(64\times81\times121=627264\)। / \(64\times81\times121=627264\).
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 \(2^4\times3^3\times5^2\times7^2\) का सही मान है?
Which option gives the correct value of \(2^4\times3^3\times5^2\times7^2\)?
#evaluate-factorisation
#number-529200
#expert
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A 529200
B 264600
C 1058400
D 415800
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\), \(3^3=27\), \(5^2=25\) और \(7^2=49\) निकालें। / Calculate \(2^4=16\), \(3^3=27\), \(5^2=25\), and \(7^2=49\).
Step 2
Why this answer is correct
\(16\times27\times25\times49=529200\)। / \(16\times27\times25\times49=529200\).
Step 3
Exam Tip
गुणा को चरणों में करें। / Do the multiplication step by step.
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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
#expert
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A \(2^5\times3^4\times5^2\times7\)
B \(32\times81\times25\times7\)
C \(2^5\times405\times35\)
D \(160\times2835\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^4\times5^2\times7\)
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 अभाज्य हैं। / In the first option, bases 2, 3, 5, and 7 are prime.
Step 3
Exam Tip
32, 81, 25, 405, 35 और 160 संयुक्त हैं, इसलिए वे अंतिम रूप नहीं हैं। / 32, 81, 25, 405, 35, and 160 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
#expert
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A \(2^6\times81\times121\)
B \(2^6\times3^4\times11^2\)
C \(2^3\times3^6\times5\times13\)
D \(3^4\times5^2\times7^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times81\times121\)
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 121 संयुक्त आधार हैं। / 81 and 121 are composite bases.
Step 3
Exam Tip
\(2^6\times81\times121\) को \(2^6\times3^4\times11^2\) में बदलना होगा। / \(2^6\times81\times121\) must be changed into \(2^6\times3^4\times11^2\).
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यदि \(2^4\times3^5\times5^2\times7\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^4\times3^5\times5^2\times7\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#expert
#mcq
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A 680400
B 340200
C 1360800
D 453600
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\), \(3^5=243\), \(5^2=25\) और (7) लें। / Take \(2^4=16\), \(3^5=243\), \(5^2=25\), and (7).
Step 2
Why this answer is correct
\(16\times243\times25\times7=680400\)। / \(16\times243\times25\times7=680400\).
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 \(2^3\times3^3\times5^2\times7\times11\) किसी संख्या का अभाज्य गुणनखंडन है, तो संख्या क्या है?
If \(2^3\times3^3\times5^2\times7\times11\) is the prime factorisation of a number, what is the number?
#evaluate-factorisation
#number-415800
#expert
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A 415800
B 207900
C 831600
D 277200
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\), \(3^3=27\) और \(5^2=25\) निकालें। / Calculate \(2^3=8\), \(3^3=27\), and \(5^2=25\).
Step 2
Why this answer is correct
\(8\times27\times25\times7\times11=415800\)। / \(8\times27\times25\times7\times11=415800\).
Step 3
Exam Tip
कई गुणनखंड हों तो छोटे समूह बनाकर गुणा करें। / When there are many factors, multiply in small groups.
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संख्या 582120 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 582120?
#prime-factorisation
#number-582120
#expert
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A \(2^4\times3^3\times5^2\times7^2\times11\)
B \(2^5\times3^2\times5^2\times7^2\times11\)
C \(16\times36382.5\)
D \(2^4\times27\times25\times49\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^3\times5^2\times7^2\times11\)
Step 1
Concept
\(582120=52920\times11\) लिखें। / Write the number using prime-base groups.
Step 2
Why this answer is correct
\(52920=2^3\times3^3\times5\times7^2\) नहीं बल्कि यहां \(16\times27\times25\times49\times11\) से \(2^4\times3^3\times5^2\times7^2\times11\) मिलता है। / \(16\times27\times25\times49\times11=2^4\times3^3\times5^2\times7^2\times11\).
Step 3
Exam Tip
दशमलव वाले विकल्प से बचें और अभाज्य आधार लिखें। / Avoid decimal-based options and write prime bases.
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संख्या 254016 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 254016?
#prime-factorisation
#number-254016
#expert
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A \(2^6\times3^4\times7^2\)
B \(2^5\times3^5\times7^2\)
C \(64\times3969\)
D \(2^6\times81\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\times3^4\times7^2\)
Step 1
Concept
\(254016=64\times3969\) लिखें। / Write \(254016=64\times3969\).
Step 2
Why this answer is correct
\(64=2^6\) और \(3969=3^4\times7^2\), इसलिए \(254016=2^6\times3^4\times7^2\)। / \(64=2^6\) and \(3969=3^4\times7^2\), so \(254016=2^6\times3^4\times7^2\).
Step 3
Exam Tip
3969 को अभाज्य घातों में बदलें। / Convert 3969 into prime powers.
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संख्या 2138400 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2138400?
#prime-factorisation
#number-2138400
#expert
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A \(2^5\times3^5\times5^2\times11\)
B \(2^6\times3^4\times5^2\times11\)
C \(32\times66825\)
D \(2^5\times243\times25\times11\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^5\times5^2\times11\)
Step 1
Concept
\(2138400=32\times66825\) लिखें। / Write \(2138400=32\times66825\).
Step 2
Why this answer is correct
\(66825=3^5\times5^2\times11\), इसलिए \(2138400=2^5\times3^5\times5^2\times11\)। / \(66825=3^5\times5^2\times11\), so \(2138400=2^5\times3^5\times5^2\times11\).
Step 3
Exam Tip
66825 को पूरा अभाज्य रूप दें। / Give 66825 its complete prime form.
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अभाज्य गुणनखंडन में \(64\times3969\) को अंतिम उत्तर क्यों नहीं माना जाएगा?
Why will \(64\times3969\) not be considered the final answer in prime factorisation?
#prime-factorisation
#concept-check
#expert
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A क्योंकि 64 और 3969 संयुक्त रूप हैं / Because 64 and 3969 are composite forms
B क्योंकि 64 अभाज्य संख्या है / Because 64 is prime
C क्योंकि 3969 को तोड़ा नहीं जा सकता / Because 3969 cannot be factorised
D क्योंकि गुणनफल बदल जाएगा / Because the product will change
Explanation opens after your attempt
Correct Answer
A. क्योंकि 64 और 3969 संयुक्त रूप हैं / Because 64 and 3969 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
\(64=2^6\) और \(3969=3^4\times7^2\) है। / \(64=2^6\) and \(3969=3^4\times7^2\).
Step 3
Exam Tip
इसलिए अंतिम रूप \(2^6\times3^4\times7^2\) होगा। / Therefore, the final form is \(2^6\times3^4\times7^2\).
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