अभाज्य गुणनखंडन का सही अर्थ क्या है?
What is the correct meaning of prime factorisation?
#prime-factorisation
#concept
#easy
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A किसी संख्या को अभाज्य संख्याओं के गुणनफल के रूप में लिखना / Writing a number as a product of prime numbers
B किसी संख्या को केवल दो भागों में बांटना / Dividing a number into only two parts
C किसी संख्या को जोड़ के रूप में लिखना / Writing a number as a sum
D किसी संख्या से 1 घटाना / Subtracting 1 from a number
Explanation opens after your attempt
Correct Answer
A. किसी संख्या को अभाज्य संख्याओं के गुणनफल के रूप में लिखना / Writing a number as a product of prime numbers
Step 1
Concept
अभाज्य गुणनखंडन में संख्या को अभाज्य संख्याओं के गुणनफल में लिखते हैं। / In prime factorisation, a number is written as a product of prime numbers.
Step 2
Why this answer is correct
जैसे 12 को \(2^2\times3\) लिखा जा सकता है। / For example, 12 can be written as \(2^2\times3\).
Step 3
Exam Tip
अंतिम रूप में केवल अभाज्य संख्याएं रखें। / Keep only prime numbers in the final form.
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संख्या 12 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 12?
#prime-factorisation
#number-12
#easy
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A \(2^2\times3\)
B \(2\times6\)
C \(3\times4\)
D \(12\times1\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\)
Step 1
Concept
12 को 2 से भाग दें तो 6 मिलता है। / Divide 12 by 2 to get 6.
Step 2
Why this answer is correct
6 का गुणनखंडन \(2\times3\) है, इसलिए \(12=2^2\times3\)। / \(6=2\times3\), so \(12=2^2\times3\).
Step 3
Exam Tip
4 और 6 संयुक्त हैं, इसलिए अंतिम उत्तर में नहीं रखें। / 4 and 6 are composite, so do not keep them in the final answer.
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संख्या 18 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 18?
#prime-factorisation
#number-18
#easy
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A \(2\times3^2\)
B \(2^2\times3\)
C \(6\times3\)
D \(9\times2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\)
Step 1
Concept
18 को \(2\times9\) लिखें। / Write 18 as \(2\times9\).
Step 2
Why this answer is correct
\(9=3^2\), इसलिए \(18=2\times3^2\)। / Since \(9=3^2\), \(18=2\times3^2\).
Step 3
Exam Tip
9 को अंतिम अभाज्य रूप में न छोड़ें। / Do not leave 9 in the final prime form.
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संख्या 20 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 20?
#prime-factorisation
#number-20
#easy
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A \(2^2\times5\)
B \(2\times10\)
C \(4\times5\)
D \(20\times1\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times5\)
Step 1
Concept
\(20=4\times5\) लिखें। / Write \(20=4\times5\).
Step 2
Why this answer is correct
\(4=2^2\), इसलिए \(20=2^2\times5\)। / Since \(4=2^2\), \(20=2^2\times5\).
Step 3
Exam Tip
4 संयुक्त संख्या है, इसलिए अंतिम रूप में \(2^2\) लिखें। / 4 is composite, so write \(2^2\) in the final form.
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संख्या 24 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 24?
#prime-factorisation
#number-24
#easy
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A \(2^3\times3\)
B \(2^2\times6\)
C \(8\times3\)
D \(4\times6\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\)
Step 1
Concept
24 को बार-बार 2 से भाग दें। / Divide 24 repeatedly by 2.
Step 2
Why this answer is correct
\(24=2\times2\times2\times3=2^3\times3\)। / \(24=2\times2\times2\times3=2^3\times3\).
Step 3
Exam Tip
8 और 6 संयुक्त हैं, इसलिए सही अभाज्य रूप नहीं हैं। / 8 and 6 are composite, so they are not the correct prime form.
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संख्या 28 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 28?
#prime-factorisation
#number-28
#easy
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A \(2^2\times7\)
B \(2\times14\)
C \(4\times7\)
D \(28\times1\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times7\)
Step 1
Concept
\(28=4\times7\) लिखें। / Write \(28=4\times7\).
Step 2
Why this answer is correct
\(4=2^2\), इसलिए \(28=2^2\times7\)। / Since \(4=2^2\), \(28=2^2\times7\).
Step 3
Exam Tip
अंतिम उत्तर में 4 की जगह \(2^2\) लिखना जरूरी है। / In the final answer, write \(2^2\) instead of 4.
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संख्या 30 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 30?
#prime-factorisation
#number-30
#easy
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A \(2\times3\times5\)
B \(6\times5\)
C \(10\times3\)
D \(15\times2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\)
Step 1
Concept
30 को \(3\times10\) लिख सकते हैं। / 30 can be written as \(3\times10\).
Step 2
Why this answer is correct
\(10=2\times5\), इसलिए \(30=2\times3\times5\)। / \(10=2\times5\), so \(30=2\times3\times5\).
Step 3
Exam Tip
6, 10 या 15 को अंतिम अभाज्य रूप में न रखें। / Do not keep 6, 10, or 15 in the final prime form.
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संख्या 36 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 36?
#prime-factorisation
#number-36
#easy
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A \(2^2\times3^2\)
B \(4\times9\)
C \(6\times6\)
D \(2\times18\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\)
Step 1
Concept
\(36=4\times9\) लिखें। / Write \(36=4\times9\).
Step 2
Why this answer is correct
\(4=2^2\) और \(9=3^2\), इसलिए \(36=2^2\times3^2\)। / \(4=2^2\) and \(9=3^2\), so \(36=2^2\times3^2\).
Step 3
Exam Tip
पूर्ण अभाज्य रूप में केवल अभाज्य आधार रखें। / In complete prime form, keep only prime bases.
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संख्या 42 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 42?
#prime-factorisation
#number-42
#easy
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A \(2\times3\times7\)
B \(6\times7\)
C \(14\times3\)
D \(21\times2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times7\)
Step 1
Concept
\(42=6\times7\) लिखें। / Write \(42=6\times7\).
Step 2
Why this answer is correct
\(6=2\times3\), इसलिए \(42=2\times3\times7\)। / \(6=2\times3\), so \(42=2\times3\times7\).
Step 3
Exam Tip
6 संयुक्त है, इसलिए उसे अंतिम उत्तर में न रखें। / 6 is composite, so do not keep it in the final answer.
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संख्या 45 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 45?
#prime-factorisation
#number-45
#easy
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A \(3^2\times5\)
B \(9\times5\)
C \(3\times15\)
D \(5^2\times3\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5\)
Step 1
Concept
\(45=9\times5\) लिखें। / Write \(45=9\times5\).
Step 2
Why this answer is correct
\(9=3^2\), इसलिए \(45=3^2\times5\)। / Since \(9=3^2\), \(45=3^2\times5\).
Step 3
Exam Tip
9 संयुक्त है, इसलिए अंतिम रूप में \(3^2\) लिखें। / 9 is composite, so write \(3^2\) in the final form.
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संख्या 48 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 48?
#prime-factorisation
#number-48
#easy
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A \(2^4\times3\)
B \(2^3\times6\)
C \(16\times3\)
D \(8\times6\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3\)
Step 1
Concept
48 को बार-बार 2 से भाग दें। / Divide 48 repeatedly by 2.
Step 2
Why this answer is correct
\(48=2^4\times3\) मिलता है। / We get \(48=2^4\times3\).
Step 3
Exam Tip
16 और 6 संयुक्त हैं, इसलिए अंतिम अभाज्य उत्तर नहीं हैं। / 16 and 6 are composite, so they are not final prime answers.
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संख्या 50 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 50?
#prime-factorisation
#number-50
#easy
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A \(2\times5^2\)
B \(2^2\times5\)
C \(10\times5\)
D \(25\times2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times5^2\)
Step 1
Concept
\(50=2\times25\) लिखें। / Write \(50=2\times25\).
Step 2
Why this answer is correct
\(25=5^2\), इसलिए \(50=2\times5^2\)। / Since \(25=5^2\), \(50=2\times5^2\).
Step 3
Exam Tip
25 संयुक्त है, इसलिए अंतिम रूप में \(5^2\) लिखें। / 25 is composite, so write \(5^2\) in the final form.
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संख्या 56 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 56?
#prime-factorisation
#number-56
#easy
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A \(2^3\times7\)
B \(8\times7\)
C \(2^2\times14\)
D \(4\times14\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times7\)
Step 1
Concept
\(56=8\times7\) लिखें। / Write \(56=8\times7\).
Step 2
Why this answer is correct
\(8=2^3\), इसलिए \(56=2^3\times7\)। / Since \(8=2^3\), \(56=2^3\times7\).
Step 3
Exam Tip
8 संयुक्त है, इसलिए अंतिम उत्तर में \(2^3\) लिखें। / 8 is composite, so write \(2^3\) in the final answer.
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संख्या 60 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 60?
#prime-factorisation
#number-60
#easy
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A \(2^2\times3\times5\)
B \(6\times10\)
C \(2\times30\)
D \(4\times15\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times5\)
Step 1
Concept
\(60=6\times10\) लिखें। / Write \(60=6\times10\).
Step 2
Why this answer is correct
\(6=2\times3\) और \(10=2\times5\), इसलिए \(60=2^2\times3\times5\)। / \(6=2\times3\) and \(10=2\times5\), so \(60=2^2\times3\times5\).
Step 3
Exam Tip
6 और 10 अंतिम अभाज्य रूप नहीं हैं। / 6 and 10 are not final prime forms.
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संख्या 63 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 63?
#prime-factorisation
#number-63
#easy
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A \(3^2\times7\)
B \(9\times7\)
C \(3\times21\)
D \(7^2\times3\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times7\)
Step 1
Concept
\(63=9\times7\) लिखें। / Write \(63=9\times7\).
Step 2
Why this answer is correct
\(9=3^2\), इसलिए \(63=3^2\times7\)। / Since \(9=3^2\), \(63=3^2\times7\).
Step 3
Exam Tip
9 या 21 संयुक्त हैं, इसलिए अंतिम उत्तर में नहीं रहेंगे। / 9 or 21 are composite, so they will not remain in the final answer.
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संख्या 72 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 72?
#prime-factorisation
#number-72
#easy
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A \(2^3\times3^2\)
B \(8\times9\)
C \(2^2\times18\)
D \(6\times12\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^2\)
Step 1
Concept
\(72=8\times9\) लिखें। / Write \(72=8\times9\).
Step 2
Why this answer is correct
\(8=2^3\) और \(9=3^2\), इसलिए \(72=2^3\times3^2\)। / \(8=2^3\) and \(9=3^2\), so \(72=2^3\times3^2\).
Step 3
Exam Tip
अभाज्य गुणनखंडन में 8 और 9 को अलग करके लिखें। / In prime factorisation, break 8 and 9 into prime powers.
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संख्या 75 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 75?
#prime-factorisation
#number-75
#easy
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A \(3\times5^2\)
B \(15\times5\)
C \(3^2\times5\)
D \(25\times3\)
Explanation opens after your attempt
Correct Answer
A. \(3\times5^2\)
Step 1
Concept
\(75=3\times25\) लिखें। / Write \(75=3\times25\).
Step 2
Why this answer is correct
\(25=5^2\), इसलिए \(75=3\times5^2\)। / Since \(25=5^2\), \(75=3\times5^2\).
Step 3
Exam Tip
25 संयुक्त है, इसलिए अंतिम रूप में \(5^2\) लिखें। / 25 is composite, so write \(5^2\) in the final form.
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संख्या 84 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 84?
#prime-factorisation
#number-84
#easy
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? Hint Small clue
A \(2^2\times3\times7\)
B \(4\times21\)
C \(2\times42\)
D \(12\times7\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3\times7\)
Step 1
Concept
\(84=4\times21\) लिखें। / Write \(84=4\times21\).
Step 2
Why this answer is correct
\(4=2^2\) और \(21=3\times7\), इसलिए \(84=2^2\times3\times7\)। / \(4=2^2\) and \(21=3\times7\), so \(84=2^2\times3\times7\).
Step 3
Exam Tip
4 और 21 को अंतिम उत्तर में न रखें। / Do not keep 4 and 21 in the final answer.
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संख्या 90 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 90?
#prime-factorisation
#number-90
#easy
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? Hint Small clue
A \(2\times3^2\times5\)
B \(9\times10\)
C \(2^2\times3\times5\)
D \(6\times15\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^2\times5\)
Step 1
Concept
\(90=9\times10\) लिखें। / Write \(90=9\times10\).
Step 2
Why this answer is correct
\(9=3^2\) और \(10=2\times5\), इसलिए \(90=2\times3^2\times5\)। / \(9=3^2\) and \(10=2\times5\), so \(90=2\times3^2\times5\).
Step 3
Exam Tip
घातों को ध्यान से लिखें, क्योंकि 3 दो बार आता है। / Write powers carefully because 3 appears twice.
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संख्या 96 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 96?
#prime-factorisation
#number-96
#easy
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? Hint Small clue
A \(2^5\times3\)
B \(32\times3\)
C \(2^4\times6\)
D \(12\times8\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3\)
Step 1
Concept
96 को बार-बार 2 से भाग दें। / Divide 96 repeatedly by 2.
Step 2
Why this answer is correct
\(96=2^5\times3\) मिलता है। / We get \(96=2^5\times3\).
Step 3
Exam Tip
32 का मतलब \(2^5\) है, लेकिन अंतिम अभाज्य रूप में आधार 2 लिखें। / 32 means \(2^5\), but in final prime form write base 2.
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संख्या 100 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 100?
#prime-factorisation
#number-100
#easy
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? Hint Small clue
A \(2^2\times5^2\)
B \(10\times10\)
C \(4\times25\)
D \(2\times50\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times5^2\)
Step 1
Concept
\(100=4\times25\) लिखें। / Write \(100=4\times25\).
Step 2
Why this answer is correct
\(4=2^2\) और \(25=5^2\), इसलिए \(100=2^2\times5^2\)। / \(4=2^2\) and \(25=5^2\), so \(100=2^2\times5^2\).
Step 3
Exam Tip
4 और 25 को अभाज्य घातों में बदलें। / Convert 4 and 25 into prime powers.
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संख्या 108 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 108?
#prime-factorisation
#number-108
#easy
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? Hint Small clue
A \(2^2\times3^3\)
B \(4\times27\)
C \(2^3\times3^2\)
D \(12\times9\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^3\)
Step 1
Concept
\(108=4\times27\) लिखें। / Write \(108=4\times27\).
Step 2
Why this answer is correct
\(4=2^2\) और \(27=3^3\), इसलिए \(108=2^2\times3^3\)। / \(4=2^2\) and \(27=3^3\), so \(108=2^2\times3^3\).
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 120 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 120?
#prime-factorisation
#number-120
#easy
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? Hint Small clue
A \(2^3\times3\times5\)
B \(12\times10\)
C \(2^2\times3\times10\)
D \(5\times24\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times5\)
Step 1
Concept
\(120=12\times10\) लिखें। / Write \(120=12\times10\).
Step 2
Why this answer is correct
\(12=2^2\times3\) और \(10=2\times5\), इसलिए \(120=2^3\times3\times5\)। / \(12=2^2\times3\) and \(10=2\times5\), so \(120=2^3\times3\times5\).
Step 3
Exam Tip
2 की कुल संख्या ध्यान से गिनें। / Count the total number of 2s carefully.
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संख्या 125 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 125?
#prime-factorisation
#number-125
#easy
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? Hint Small clue
A \(5^3\)
B \(25\times5\)
C \(5^2\)
D \(125\times1\)
Explanation opens after your attempt
Correct Answer
A. \(5^3\)
Step 1
Concept
125 को 5 से भाग दें तो 25 मिलता है। / Divide 125 by 5 to get 25.
Step 2
Why this answer is correct
\(25=5^2\), इसलिए \(125=5^3\)। / \(25=5^2\), so \(125=5^3\).
Step 3
Exam Tip
25 संयुक्त है, इसलिए अंतिम रूप \(5^3\) है। / 25 is composite, so the final form is \(5^3\).
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संख्या 144 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 144?
#prime-factorisation
#number-144
#easy
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? Hint Small clue
A \(2^4\times3^2\)
B \(12\times12\)
C \(2^3\times3^3\)
D \(16\times9\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^2\)
Step 1
Concept
\(144=16\times9\) लिखें। / Write \(144=16\times9\).
Step 2
Why this answer is correct
\(16=2^4\) और \(9=3^2\), इसलिए \(144=2^4\times3^2\)। / \(16=2^4\) and \(9=3^2\), so \(144=2^4\times3^2\).
Step 3
Exam Tip
पूर्ण वर्ग संख्याओं में घातें सम हो सकती हैं, इसलिए घातों को जांचें। / Perfect square numbers can have even exponents, so check the powers.
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यदि \(72=2^a\times3^2\), तो (a) का मान क्या है?
If \(72=2^a\times3^2\), what is the value of (a)?
#exponent-comparison
#prime-factorisation
#easy
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A 3
B 2
C 4
D 1
Explanation opens after your attempt
Step 1
Concept
72 का अभाज्य गुणनखंडन \(2^3\times3^2\) है। / The prime factorisation of 72 is \(2^3\times3^2\).
Step 2
Why this answer is correct
दिए गए रूप से तुलना करने पर 2 की घात (a) है। / Comparing with the given form, the power of 2 is (a).
Step 3
Exam Tip
इसलिए (a=3) होगा। / Therefore, (a=3).
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यदि \(90=2\times3^b\times5\), तो (b) का मान क्या है?
If \(90=2\times3^b\times5\), what is the value of (b)?
#exponent-comparison
#prime-factorisation
#easy
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? Hint Small clue
A 2
B 1
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
90 का अभाज्य गुणनखंडन \(2\times3^2\times5\) है। / The prime factorisation of 90 is \(2\times3^2\times5\).
Step 2
Why this answer is correct
दिए गए रूप में 3 की घात (b) है। / In the given form, the power of 3 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 \(2^2\times3\times5\) है?
Which number has prime factorisation \(2^2\times3\times5\)?
#evaluate-factorisation
#number-60
#easy
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A 60
B 30
C 90
D 120
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\) निकालें। / Calculate \(2^2=4\).
Step 2
Why this answer is correct
\(4\times3\times5=60\)। / \(4\times3\times5=60\).
Step 3
Exam Tip
अभाज्य गुणनखंडन से संख्या पाने के लिए सभी गुणनखंडों का गुणा करें। / To get the number from prime factorisation, multiply all factors.
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किस संख्या का अभाज्य गुणनखंडन \(2^3\times3^2\) है?
Which number has prime factorisation \(2^3\times3^2\)?
#evaluate-factorisation
#number-72
#easy
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? Hint Small clue
A 72
B 48
C 54
D 96
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
\(8\times9=72\)। / \(8\times9=72\).
Step 3
Exam Tip
घातों का मान पहले निकालने से उत्तर जल्दी मिलता है। / Evaluating powers first gives the answer quickly.
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यदि \(n=2^3\times5\), तो (n) का मान क्या है?
If \(n=2^3\times5\), what is the value of (n)?
#evaluate-factorisation
#powers
#easy
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? Hint Small clue
A 40
B 30
C 20
D 50
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) है। / \(2^3=8\).
Step 2
Why this answer is correct
\(8\times5=40\)। / \(8\times5=40\).
Step 3
Exam Tip
अभाज्य गुणनखंडन को संख्या में बदलने के लिए गुणा करें। / Multiply the factors to convert prime factorisation into the number.
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यदि \(m=3^2\times7\), तो (m) का मान क्या है?
If \(m=3^2\times7\), what is the value of (m)?
#evaluate-factorisation
#powers
#easy
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? Hint Small clue
A 63
B 42
C 72
D 84
Explanation opens after your attempt
Step 1
Concept
\(3^2=9\) है। / \(3^2=9\).
Step 2
Why this answer is correct
\(9\times7=63\)। / \(9\times7=63\).
Step 3
Exam Tip
घात वाले रूप में पहले घात का मान निकालें। / In an expression with powers, evaluate the 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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? Hint Small clue
A \(2\times3\times5\)
B \(4\times3\times5\)
C \(2\times6\times5\)
D \(10\times3\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\)
Step 1
Concept
अभाज्य गुणनखंड में हर संख्या अभाज्य होनी चाहिए। / In prime factorisation, every factor must be prime.
Step 2
Why this answer is correct
2, 3 और 5 अभाज्य हैं। / 2, 3, and 5 are prime.
Step 3
Exam Tip
4, 6 और 10 संयुक्त हैं, इसलिए वे अंतिम अभाज्य रूप में नहीं रह सकते। / 4, 6, and 10 are composite, so they cannot remain in the final prime 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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? Hint Small clue
A \(4\times3\times5\)
B \(2^2\times3\times5\)
C \(2\times3\times7\)
D \(3^2\times5\)
Explanation opens after your attempt
Correct Answer
A. \(4\times3\times5\)
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में संयुक्त संख्या नहीं होनी चाहिए। / A final prime factorisation must not contain a composite number.
Step 2
Why this answer is correct
4 संयुक्त संख्या है, इसलिए \(4\times3\times5\) अंतिम रूप नहीं है। / 4 is composite, so \(4\times3\times5\) is not final form.
Step 3
Exam Tip
4 को \(2^2\) में बदलें। / Change 4 into \(2^2\).
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संख्या 64 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 64?
#prime-factorisation
#power-of-two
#easy
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A \(2^6\)
B \(2^5\)
C \(4^3\)
D \(8^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\)
Step 1
Concept
64 को बार-बार 2 से भाग दें। / Divide 64 repeatedly by 2.
Step 2
Why this answer is correct
छह बार 2 मिलने से \(64=2^6\) होता है। / Six factors of 2 give \(64=2^6\).
Step 3
Exam Tip
4 और 8 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप में नहीं लिखें। / 4 and 8 are composite, so do not write them in final prime form.
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संख्या 81 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 81?
#prime-factorisation
#power-of-three
#easy
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? Hint Small clue
A \(3^4\)
B \(3^3\)
C \(9^2\)
D \(27\times3\)
Explanation opens after your attempt
Correct Answer
A. \(3^4\)
Step 1
Concept
81 को 3 से बार-बार भाग दें। / Divide 81 repeatedly by 3.
Step 2
Why this answer is correct
चार बार 3 मिलने से \(81=3^4\)। / Four factors of 3 give \(81=3^4\).
Step 3
Exam Tip
9 और 27 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप में 3 की घात लिखें। / 9 and 27 are composite, so write the power of 3 in final prime form.
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संख्या 121 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 121?
#prime-factorisation
#square-number
#easy
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? Hint Small clue
A \(11^2\)
B \(11\times12\)
C \(121\times1\)
D \(7\times17\)
Explanation opens after your attempt
Correct Answer
A. \(11^2\)
Step 1
Concept
121 एक वर्ग संख्या है। / 121 is a square number.
Step 2
Why this answer is correct
\(121=11\times11=11^2\)। / \(121=11\times11=11^2\).
Step 3
Exam Tip
11 अभाज्य है, इसलिए \(11^2\) सही अभाज्य गुणनखंडन है। / Since 11 is prime, \(11^2\) is the correct prime factorisation.
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संख्या 49 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 49?
#prime-factorisation
#square-number
#easy
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? Hint Small clue
A \(7^2\)
B \(7\times6\)
C \(49\times1\)
D \(5\times9\)
Explanation opens after your attempt
Correct Answer
A. \(7^2\)
Step 1
Concept
49 को \(7\times7\) लिखा जा सकता है। / 49 can be written as \(7\times7\).
Step 2
Why this answer is correct
7 अभाज्य संख्या है, इसलिए \(49=7^2\)। / Since 7 is prime, \(49=7^2\).
Step 3
Exam Tip
वर्ग संख्या में समान अभाज्य दो बार आ सकता है। / In a square number, the same prime may appear twice.
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संख्या 27 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 27?
#prime-factorisation
#cube-number
#easy
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? Hint Small clue
A \(3^3\)
B \(3^2\)
C \(9\times3\)
D \(27\times1\)
Explanation opens after your attempt
Correct Answer
A. \(3^3\)
Step 1
Concept
27 को \(3\times9\) लिखें। / Write 27 as \(3\times9\).
Step 2
Why this answer is correct
\(9=3^2\), इसलिए \(27=3^3\)। / Since \(9=3^2\), \(27=3^3\).
Step 3
Exam Tip
9 संयुक्त है, इसलिए अंतिम रूप \(3^3\) है। / 9 is composite, so the final form is \(3^3\).
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संख्या 32 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 32?
#prime-factorisation
#power-of-two
#easy
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? Hint Small clue
A \(2^5\)
B \(2^4\)
C \(4^2\)
D \(8\times4\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\)
Step 1
Concept
32 को 2 से बार-बार भाग दें। / Divide 32 repeatedly by 2.
Step 2
Why this answer is correct
पांच बार 2 मिलने से \(32=2^5\) होता है। / Five factors of 2 give \(32=2^5\).
Step 3
Exam Tip
4 और 8 संयुक्त हैं, इसलिए अंतिम रूप में नहीं लिखें। / 4 and 8 are composite, so do not write them in final form.
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संख्या 16 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 16?
#prime-factorisation
#power-of-two
#easy
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? Hint Small clue
A \(2^4\)
B \(4^2\)
C \(2^3\)
D \(8\times2\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\)
Step 1
Concept
16 को \(2\times2\times2\times2\) लिखा जाता है। / 16 is \(2\times2\times2\times2\).
Step 2
Why this answer is correct
इसलिए \(16=2^4\)। / Therefore, \(16=2^4\).
Step 3
Exam Tip
4 और 8 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप में 2 की घात लिखें। / 4 and 8 are composite, so write the power of 2 in final prime form.
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संख्या 25 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 25?
#prime-factorisation
#square-number
#easy
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A \(5^2\)
B \(5\times4\)
C \(25\times1\)
D \(3\times8\)
Explanation opens after your attempt
Correct Answer
A. \(5^2\)
Step 1
Concept
25 को \(5\times5\) लिखा जाता है। / 25 is \(5\times5\).
Step 2
Why this answer is correct
5 अभाज्य है, इसलिए \(25=5^2\)। / Since 5 is prime, \(25=5^2\).
Step 3
Exam Tip
समान अभाज्य दो बार आए तो घात 2 लिखें। / If the same prime appears twice, write power 2.
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संख्या 80 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 80?
#prime-factorisation
#number-80
#easy
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? Hint Small clue
A \(2^4\times5\)
B \(2^3\times10\)
C \(16\times5\)
D \(8\times10\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times5\)
Step 1
Concept
\(80=16\times5\) लिखें। / Write \(80=16\times5\).
Step 2
Why this answer is correct
\(16=2^4\), इसलिए \(80=2^4\times5\)। / Since \(16=2^4\), \(80=2^4\times5\).
Step 3
Exam Tip
16 संयुक्त है, इसलिए उसे \(2^4\) के रूप में बदलें। / 16 is composite, so change it into \(2^4\).
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संख्या 98 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 98?
#prime-factorisation
#number-98
#easy
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? Hint Small clue
A \(2\times7^2\)
B \(2^2\times7\)
C \(14\times7\)
D \(49\times2\)
Explanation opens after your attempt
Correct Answer
A. \(2\times7^2\)
Step 1
Concept
\(98=2\times49\) लिखें। / Write \(98=2\times49\).
Step 2
Why this answer is correct
\(49=7^2\), इसलिए \(98=2\times7^2\)। / Since \(49=7^2\), \(98=2\times7^2\).
Step 3
Exam Tip
49 संयुक्त है, इसलिए अंतिम रूप में \(7^2\) लिखें। / 49 is composite, so write \(7^2\) in the final form.
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संख्या 105 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 105?
#prime-factorisation
#number-105
#easy
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? Hint Small clue
A \(3\times5\times7\)
B \(15\times7\)
C \(21\times5\)
D \(35\times3\)
Explanation opens after your attempt
Correct Answer
A. \(3\times5\times7\)
Step 1
Concept
\(105=15\times7\) लिखें। / Write \(105=15\times7\).
Step 2
Why this answer is correct
\(15=3\times5\), इसलिए \(105=3\times5\times7\)। / \(15=3\times5\), so \(105=3\times5\times7\).
Step 3
Exam Tip
15, 21 और 35 संयुक्त हैं, इसलिए उन्हें अंतिम उत्तर में न रखें। / 15, 21, and 35 are composite, so do not keep them in the final answer.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^2\times3^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^2\times3^2\), which number is it?
#evaluate-factorisation
#number-36
#easy
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? Hint Small clue
A 36
B 24
C 48
D 72
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
\(4\times9=36\)। / \(4\times9=36\).
Step 3
Exam Tip
अभाज्य गुणनखंडन से संख्या पाने के लिए गुणा करें। / Multiply to get the number from prime factorisation.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2\times5^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2\times5^2\), which number is it?
#evaluate-factorisation
#number-50
#easy
50 50-50 2 wrong hide
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A 50
B 25
C 40
D 100
Explanation opens after your attempt
Step 1
Concept
\(5^2=25\) है। / \(5^2=25\).
Step 2
Why this answer is correct
\(2\times25=50\)। / \(2\times25=50\).
Step 3
Exam Tip
घात का मान निकालकर फिर गुणा करें। / Find the value of the power and then multiply.
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किस संख्या का अभाज्य गुणनखंडन \(2\times3\times7\) है?
Which number has prime factorisation \(2\times3\times7\)?
#evaluate-factorisation
#number-42
#easy
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A 42
B 21
C 56
D 84
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Step 1
Concept
अभाज्य गुणनखंड दिए गए हैं। / The prime factors are given.
Step 2
Why this answer is correct
\(2\times3\times7=42\)। / \(2\times3\times7=42\).
Step 3
Exam Tip
जब घात न हो तो प्रत्येक 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 \(3\times5^2\) है?
Which number has prime factorisation \(3\times5^2\)?
#evaluate-factorisation
#number-75
#easy
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A 75
B 45
C 90
D 150
Explanation opens after your attempt
Step 1
Concept
\(5^2=25\) निकालें। / Calculate \(5^2=25\).
Step 2
Why this answer is correct
\(3\times25=75\)। / \(3\times25=75\).
Step 3
Exam Tip
घात को पहले सरल करें, फिर गुणा करें। / Simplify the power first and then multiply.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4\times3\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^4\times3\), which number is it?
#evaluate-factorisation
#number-48
#easy
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A 48
B 24
C 64
D 96
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) निकालें। / Calculate \(2^4=16\).
Step 2
Why this answer is correct
\(16\times3=48\)। / \(16\times3=48\).
Step 3
Exam Tip
अभाज्य घात का मान पहले निकालना आसान रहता है। / It is easier to find the value of prime powers first.
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अभाज्य गुणनखंडन करते समय अंतिम रूप में कौन सा गुणनखंड नहीं रहना चाहिए?
While doing prime factorisation, which type of factor should not remain in the final form?
#prime-factorisation
#concept-check
#easy
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A संयुक्त गुणनखंड / Composite factor
B अभाज्य गुणनखंड / Prime factor
C 2 जैसा अभाज्य गुणनखंड / Prime factor like 2
D 3 जैसा अभाज्य गुणनखंड / Prime factor like 3
Explanation opens after your attempt
Correct Answer
A. संयुक्त गुणनखंड / Composite factor
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में केवल अभाज्य संख्याएं रहती हैं। / A final prime factorisation contains only prime numbers.
Step 2
Why this answer is correct
संयुक्त गुणनखंड को आगे तोड़ना जरूरी होता है। / A composite factor must be broken further.
Step 3
Exam Tip
परीक्षा में 6, 8, 10 जैसे गुणनखंडों को अंत में न छोड़ें। / In exams, do not leave factors like 6, 8, or 10 at the end.
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