संख्या 486 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 486?
#prime-factorisation
#number-486
#easy
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A \(2\times3^5\)
B \(2^2\times3^4\)
C \(6\times81\)
D \(18\times27\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3^5\)
Step 1
Concept
\(486=2\times243\) लिखें। / Write \(486=2\times243\).
Step 2
Why this answer is correct
\(243=3^5\), इसलिए \(486=2\times3^5\)। / Since \(243=3^5\), \(486=2\times3^5\).
Step 3
Exam Tip
243 को अंतिम उत्तर में न छोड़कर 3 की घात में लिखें। / Do not leave 243 in the final answer; write it as a power of 3.
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संख्या 600 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 600?
#prime-factorisation
#number-600
#easy
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A \(2^3\times3\times5^2\)
B \(2^2\times3\times5^2\)
C \(6\times100\)
D \(2\times300\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times5^2\)
Step 1
Concept
\(600=6\times100\) लिखें। / Write \(600=6\times100\).
Step 2
Why this answer is correct
\(6=2\times3\) और \(100=2^2\times5^2\), इसलिए \(600=2^3\times3\times5^2\)। / \(6=2\times3\) and \(100=2^2\times5^2\), so \(600=2^3\times3\times5^2\).
Step 3
Exam Tip
2 की कुल घात गिनते समय सावधानी रखें। / Be careful while counting the total power of 2.
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संख्या 675 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 675?
#prime-factorisation
#number-675
#easy
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A \(3^3\times5^2\)
B \(3^2\times5^3\)
C \(27\times25\)
D \(9\times75\)
Explanation opens after your attempt
Correct Answer
A. \(3^3\times5^2\)
Step 1
Concept
\(675=27\times25\) लिखें। / Write \(675=27\times25\).
Step 2
Why this answer is correct
\(27=3^3\) और \(25=5^2\), इसलिए \(675=3^3\times5^2\)। / \(27=3^3\) and \(25=5^2\), so \(675=3^3\times5^2\).
Step 3
Exam Tip
27 और 25 संयुक्त हैं, इसलिए उन्हें अभाज्य घातों में बदलें। / 27 and 25 are composite, so convert them into prime powers.
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संख्या 720 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 720?
#prime-factorisation
#number-720
#easy
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A \(2^4\times3^2\times5\)
B \(2^3\times3^2\times5\)
C \(72\times10\)
D \(8\times90\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^2\times5\)
Step 1
Concept
\(720=72\times10\) लिखें। / Write \(720=72\times10\).
Step 2
Why this answer is correct
\(72=2^3\times3^2\) और \(10=2\times5\), इसलिए \(720=2^4\times3^2\times5\)। / \(72=2^3\times3^2\) and \(10=2\times5\), so \(720=2^4\times3^2\times5\).
Step 3
Exam Tip
72 को पूरी तरह अभाज्य रूप में तोड़ें। / Break 72 completely into prime form.
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संख्या 756 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 756?
#prime-factorisation
#number-756
#easy
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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
28 को \(2^2\times7\) में बदलें। / Convert 28 into \(2^2\times7\).
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संख्या 784 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 784?
#prime-factorisation
#square-number
#easy
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A \(2^4\times7^2\)
B \(2^3\times7^2\)
C \(28\times28\)
D \(16\times49\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times7^2\)
Step 1
Concept
\(784=28^2\) पहचाना जा सकता है। / Recognise \(784=28^2\).
Step 2
Why this answer is correct
\(28=2^2\times7\), इसलिए \(784=2^4\times7^2\)। / Since \(28=2^2\times7\), \(784=2^4\times7^2\).
Step 3
Exam Tip
वर्ग संख्या में घातें सम हो सकती हैं, इसलिए घातों को जांचें। / In a square number, exponents may be even, so check the powers.
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संख्या 840 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 840?
#prime-factorisation
#number-840
#easy
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A \(2^3\times3\times5\times7\)
B \(2^2\times3\times5\times7\)
C \(84\times10\)
D \(21\times40\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3\times5\times7\)
Step 1
Concept
\(840=84\times10\) लिखें। / Write \(840=84\times10\).
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
सभी संयुक्त गुणनखंडों को अभाज्य संख्याओं तक तोड़ें। / Break all composite factors down to primes.
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संख्या 900 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 900?
#prime-factorisation
#square-number
#easy
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A \(2^2\times3^2\times5^2\)
B \(2^3\times3^2\times5\)
C \(30\times30\)
D \(9\times100\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times5^2\)
Step 1
Concept
\(900=9\times100\) लिखें। / Write \(900=9\times100\).
Step 2
Why this answer is correct
\(9=3^2\) और \(100=2^2\times5^2\), इसलिए \(900=2^2\times3^2\times5^2\)। / \(9=3^2\) and \(100=2^2\times5^2\), so \(900=2^2\times3^2\times5^2\).
Step 3
Exam Tip
900 वर्ग संख्या है, इसलिए घातों में समता दिखती है। / 900 is a square number, so even exponents appear.
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संख्या 945 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 945?
#prime-factorisation
#number-945
#easy
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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 1000 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1000?
#prime-factorisation
#cube-number
#easy
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A \(2^3\times5^3\)
B \(2^2\times5^3\)
C \(10^3\)
D \(100\times10\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times5^3\)
Step 1
Concept
\(1000=10^3\) लिखा जा सकता है। / (1000) can be written as \(10^3\).
Step 2
Why this answer is correct
\(10=2\times5\), इसलिए \(1000=2^3\times5^3\)। / Since \(10=2\times5\), \(1000=2^3\times5^3\).
Step 3
Exam Tip
10 संयुक्त है, इसलिए अंतिम अभाज्य रूप में 2 और 5 लिखें। / 10 is composite, so write 2 and 5 in the final prime form.
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संख्या 1024 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1024?
#prime-factorisation
#power-of-two
#easy
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A \(2^{10}\)
B \(2^9\)
C \(4^5\)
D \(32^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^{10}\)
Step 1
Concept
1024 को बार-बार 2 से भाग दें। / Divide 1024 repeatedly by 2.
Step 2
Why this answer is correct
दस बार 2 मिलने से \(1024=2^{10}\) होता है। / Ten factors of 2 give \(1024=2^{10}\).
Step 3
Exam Tip
4 और 32 संयुक्त हैं, इसलिए अंतिम अभाज्य रूप में 2 की घात लिखें। / 4 and 32 are composite, so write the power of 2 in final prime form.
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संख्या 1155 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1155?
#prime-factorisation
#number-1155
#easy
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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। / 105 is composite, so break it further.
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संख्या 1176 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1176?
#prime-factorisation
#number-1176
#easy
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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 दोनों को अभाज्य रूप में लिखें। / Write both 24 and 49 in prime form.
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संख्या 1225 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1225?
#prime-factorisation
#square-number
#easy
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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
35 संयुक्त है, इसलिए अभाज्य आधार 5 और 7 लिखें। / 35 is composite, so write prime bases 5 and 7.
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संख्या 1296 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1296?
#prime-factorisation
#square-number
#easy
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A \(2^4\times3^4\)
B \(36\times36\)
C \(2^3\times3^5\)
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 अभाज्य घातों में बदलें। / Convert 16 and 81 into prime powers.
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संख्या 1323 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1323?
#prime-factorisation
#number-1323
#easy
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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 को अंतिम रूप में न छोड़ें। / Do not leave 27 and 49 in the final form.
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संख्या 1440 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1440?
#prime-factorisation
#number-1440
#easy
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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, इसे ध्यान से गिनें। / The total power of 2 is 5, so count it carefully.
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संख्या 1575 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1575?
#prime-factorisation
#number-1575
#easy
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? Hint Small clue
A \(3^2\times5^2\times7\)
B \(3\times5^3\times7\)
C \(15\times105\)
D \(225\times7\)
Explanation opens after your attempt
Correct Answer
A. \(3^2\times5^2\times7\)
Step 1
Concept
\(1575=225\times7\) लिखें। / Write \(1575=225\times7\).
Step 2
Why this answer is correct
\(225=3^2\times5^2\), इसलिए \(1575=3^2\times5^2\times7\)। / \(225=3^2\times5^2\), so \(1575=3^2\times5^2\times7\).
Step 3
Exam Tip
225 को अभाज्य घातों में बदलें। / Convert 225 into prime powers.
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संख्या 1728 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1728?
#prime-factorisation
#cube-number
#easy
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? Hint Small clue
A \(2^6\times3^3\)
B \(12^3\)
C \(2^5\times3^4\)
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 अभाज्य रूप में 2 और 3 की घातें लिखें। / 12 is composite, so write powers of 2 and 3 in the final prime form.
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संख्या 1764 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1764?
#prime-factorisation
#square-number
#easy
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? Hint Small clue
A \(2^2\times3^2\times7^2\)
B \(42\times42\)
C \(2^3\times3^2\times7\)
D \(4\times441\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\times3^2\times7^2\)
Step 1
Concept
\(1764=42^2\) है। / \(1764=42^2\).
Step 2
Why this answer is correct
\(42=2\times3\times7\), इसलिए \(1764=2^2\times3^2\times7^2\)। / Since \(42=2\times3\times7\), \(1764=2^2\times3^2\times7^2\).
Step 3
Exam Tip
वर्ग संख्या में प्रत्येक अभाज्य की घात सम होनी चाहिए। / In a square number, each prime power should be even.
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संख्या 1800 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1800?
#prime-factorisation
#number-1800
#easy
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? Hint Small clue
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 को अलग-अलग अभाज्य रूप में तोड़ें। / Break 18 and 100 separately into prime form.
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संख्या 2025 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 2025?
#prime-factorisation
#number-2025
#easy
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A \(3^4\times5^2\)
B \(3^2\times5^4\)
C \(81\times25\)
D \(45\times45\)
Explanation opens after your attempt
Correct Answer
A. \(3^4\times5^2\)
Step 1
Concept
\(2025=81\times25\) लिखें। / Write \(2025=81\times25\).
Step 2
Why this answer is correct
\(81=3^4\) और \(25=5^2\), इसलिए \(2025=3^4\times5^2\)। / \(81=3^4\) and \(25=5^2\), so \(2025=3^4\times5^2\).
Step 3
Exam Tip
81 और 25 को अभाज्य घातों में बदलें। / Convert 81 and 25 into prime powers.
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संख्या 2187 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2187?
#prime-factorisation
#power-of-three
#easy
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A \(3^7\)
B \(3^6\)
C \(9^3\times3\)
D \(27^2\times3\)
Explanation opens after your attempt
Correct Answer
A. \(3^7\)
Step 1
Concept
2187 को 3 से बार-बार भाग दें। / Divide 2187 repeatedly by 3.
Step 2
Why this answer is correct
सात बार 3 मिलने से \(2187=3^7\)। / Seven factors of 3 give \(2187=3^7\).
Step 3
Exam Tip
9 और 27 संयुक्त हैं, इसलिए अंतिम रूप में आधार 3 रखें। / 9 and 27 are composite, so keep base 3 in the final form.
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संख्या 2401 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 2401?
#prime-factorisation
#power-of-seven
#easy
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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। / 49 is composite, so write the power of 7 in final prime form.
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संख्या 2500 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2500?
#prime-factorisation
#number-2500
#easy
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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 है, इसे ध्यान से गिनें। / The total power of 5 is 4, so count carefully.
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यदि \(600=2^a\times3\times5^2\), तो (a) का मान क्या है?
If \(600=2^a\times3\times5^2\), what is the value of (a)?
#exponent-comparison
#prime-factorisation
#easy
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A 3
B 2
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
600 का अभाज्य गुणनखंडन \(2^3\times3\times5^2\) है। / The prime factorisation of 600 is \(2^3\times3\times5^2\).
Step 2
Why this answer is correct
दिए गए रूप में 2 की घात (a) है। / In the given form, the power of 2 is (a).
Step 3
Exam Tip
तुलना करने पर (a=3) मिलता है। / Comparing gives (a=3).
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यदि \(675=3^a\times5^2\), तो (a) का मान क्या है?
If \(675=3^a\times5^2\), what is the value of (a)?
#exponent-comparison
#prime-factorisation
#easy
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A 3
B 2
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
\(675=27\times25\) है। / \(675=27\times25\).
Step 2
Why this answer is correct
\(27=3^3\) और \(25=5^2\), इसलिए \(675=3^3\times5^2\)। / \(27=3^3\) and \(25=5^2\), so \(675=3^3\times5^2\).
Step 3
Exam Tip
तुलना करने पर (a=3) है। / Comparing gives (a=3).
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किस संख्या का अभाज्य गुणनखंडन \(2^4\times3^2\times5\) है?
Which number has prime factorisation \(2^4\times3^2\times5\)?
#evaluate-factorisation
#number-720
#easy
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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
पहले घातों का मान निकालने से गणना आसान होती है। / Evaluating powers first makes calculation easier.
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किस संख्या का अभाज्य गुणनखंडन \(2\times3^4\) है?
Which number has prime factorisation \(2\times3^4\)?
#evaluate-factorisation
#number-162
#easy
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A 162
B 81
C 324
D 486
Explanation opens after your attempt
Step 1
Concept
\(3^4=81\) निकालें। / Calculate \(3^4=81\).
Step 2
Why this answer is correct
\(2\times81=162\)। / \(2\times81=162\).
Step 3
Exam Tip
घात वाले गुणनखंड को पहले सरल करें। / Simplify the factor with a power first.
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यदि \(n=2^3\times3\times7\), तो (n) का मान क्या है?
If \(n=2^3\times3\times7\), what is the value of (n)?
#evaluate-factorisation
#powers
#easy
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A 168
B 84
C 126
D 336
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) है। / \(2^3=8\).
Step 2
Why this answer is correct
\(8\times3\times7=168\)। / \(8\times3\times7=168\).
Step 3
Exam Tip
अभाज्य गुणनखंडन से संख्या पाने के लिए गुणा करें। / Multiply to get the number from prime factorisation.
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यदि \(m=3^2\times5^2\), तो (m) का मान क्या है?
If \(m=3^2\times5^2\), what is the value of (m)?
#evaluate-factorisation
#powers
#easy
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A 225
B 150
C 300
D 450
Explanation opens after your attempt
Step 1
Concept
\(3^2=9\) और \(5^2=25\) हैं। / \(3^2=9\) and \(5^2=25\).
Step 2
Why this answer is correct
\(9\times25=225\)। / \(9\times25=225\).
Step 3
Exam Tip
दोनों घातों को पहले सरल करें। / Simplify both powers first.
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किस विकल्प में केवल अभाज्य गुणनखंड दिए गए हैं?
Which option contains only prime factors?
#prime-factors
#concept-check
#easy
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A \(2\times3\times5\times7\times11\)
B \(6\times5\times7\times11\)
C \(21\times5\times11\)
D \(2\times35\times33\)
Explanation opens after your attempt
Correct Answer
A. \(2\times3\times5\times7\times11\)
Step 1
Concept
अंतिम अभाज्य गुणनखंडन में हर गुणनखंड अभाज्य होना चाहिए। / In final prime factorisation, every factor must be prime.
Step 2
Why this answer is correct
2, 3, 5, 7 और 11 अभाज्य हैं। / 2, 3, 5, 7, and 11 are prime.
Step 3
Exam Tip
6, 21, 35 और 33 संयुक्त हैं, इसलिए वे अंतिम रूप में नहीं रह सकते। / 6, 21, 35, and 33 are composite, so they cannot remain in final form.
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किस विकल्प में अंतिम अभाज्य गुणनखंडन नहीं दिया गया है?
Which option is not a final prime factorisation?
#prime-factorisation
#not-final-form
#easy
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A \(10\times3^2\times7\)
B \(2\times3^2\times5\times7\)
C \(2^2\times3\times11\)
D \(3^3\times5^2\)
Explanation opens after your attempt
Correct Answer
A. \(10\times3^2\times7\)
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
10 संयुक्त संख्या है, इसलिए \(10\times3^2\times7\) अंतिम रूप नहीं है। / 10 is composite, so \(10\times3^2\times7\) is not final form.
Step 3
Exam Tip
10 को \(2\times5\) में बदलें। / Change 10 into \(2\times5\).
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संख्या 2048 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 2048?
#prime-factorisation
#power-of-two
#easy
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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 की घात लिखें। / 4, 32, and 64 are composite, so write the power of 2 in final form.
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संख्या 729 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 729?
#prime-factorisation
#power-of-three
#easy
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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 अभाज्य आधार 3 रखें। / 9 and 27 are composite, so keep prime base 3.
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संख्या 361 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 361?
#prime-factorisation
#square-number
#easy
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A \(19^2\)
B \(19\times18\)
C \(361\times1\)
D \(17\times21\)
Explanation opens after your attempt
Correct Answer
A. \(19^2\)
Step 1
Concept
\(361=19\times19\) है। / \(361=19\times19\).
Step 2
Why this answer is correct
19 अभाज्य संख्या है, इसलिए \(361=19^2\)। / Since 19 is prime, \(361=19^2\).
Step 3
Exam Tip
वर्ग संख्या में समान अभाज्य दो बार आता है। / In a square number, the same prime appears twice.
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संख्या 1331 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1331?
#prime-factorisation
#cube-number
#easy
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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। / 121 is composite, so write \(11^3\) in the final form.
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संख्या 4096 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 4096?
#prime-factorisation
#power-of-two
#easy
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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 \(4096=2^{12}\)। / 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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संख्या 3125 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 3125?
#prime-factorisation
#power-of-five
#easy
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A \(5^5\)
B \(5^4\)
C \(25^2\times5\)
D \(125\times25\)
Explanation opens after your attempt
Correct Answer
A. \(5^5\)
Step 1
Concept
\(3125=5\times625\) लिखें। / Write \(3125=5\times625\).
Step 2
Why this answer is correct
\(625=5^4\), इसलिए \(3125=5^5\)। / Since \(625=5^4\), \(3125=5^5\).
Step 3
Exam Tip
25 और 125 संयुक्त रूप हैं, इसलिए अंतिम उत्तर में 5 की घात लिखें। / 25 and 125 are composite forms, so write a power of 5 in the final answer.
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संख्या 2744 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 2744?
#prime-factorisation
#cube-number
#easy
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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। / 14 is composite, so write prime bases in the final form.
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संख्या 1536 का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of 1536?
#prime-factorisation
#number-1536
#easy
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? Hint Small clue
A \(2^9\times3\)
B \(2^8\times3\)
C \(512\times3\)
D \(2^6\times24\)
Explanation opens after your attempt
Correct Answer
A. \(2^9\times3\)
Step 1
Concept
\(1536=512\times3\) लिखें। / Write \(1536=512\times3\).
Step 2
Why this answer is correct
\(512=2^9\), इसलिए \(1536=2^9\times3\)। / \(512=2^9\), so \(1536=2^9\times3\).
Step 3
Exam Tip
512 को अंतिम रूप में न रखकर \(2^9\) लिखें। / Do not keep 512 in the final form; write \(2^9\).
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संख्या 1080 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1080?
#prime-factorisation
#number-1080
#easy
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? Hint Small clue
A \(2^3\times3^3\times5\)
B \(2^2\times3^3\times5\)
C \(108\times10\)
D \(27\times40\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\times3^3\times5\)
Step 1
Concept
\(1080=108\times10\) लिखें। / Write \(1080=108\times10\).
Step 2
Why this answer is correct
\(108=2^2\times3^3\) और \(10=2\times5\), इसलिए \(1080=2^3\times3^3\times5\)। / \(108=2^2\times3^3\) and \(10=2\times5\), so \(1080=2^3\times3^3\times5\).
Step 3
Exam Tip
2 और 3 की घातें अलग-अलग गिनें। / Count powers of 2 and 3 separately.
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संख्या 1470 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 1470?
#prime-factorisation
#number-1470
#easy
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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 \(7^2\) में बदलें। / Convert 49 into \(7^2\).
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संख्या 1980 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 1980?
#prime-factorisation
#number-1980
#easy
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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 किसी संख्या का अभाज्य गुणनखंडन \(2^3\times3\times7^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^3\times3\times7^2\), which number is it?
#evaluate-factorisation
#number-1176
#easy
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A 1176
B 588
C 1470
D 2352
Explanation opens after your attempt
Step 1
Concept
\(2^3=8\) और \(7^2=49\) निकालें। / Calculate \(2^3=8\) and \(7^2=49\).
Step 2
Why this answer is correct
\(8\times3\times49=1176\)। / \(8\times3\times49=1176\).
Step 3
Exam Tip
घातों का मान पहले निकालना गणना को आसान बनाता है। / Evaluating powers first makes calculation easier.
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यदि किसी संख्या का अभाज्य गुणनखंडन \(5^2\times7^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(5^2\times7^2\), which number is it?
#evaluate-factorisation
#number-1225
#easy
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A 1225
B 875
C 2450
D 6125
Explanation opens after your attempt
Step 1
Concept
\(5^2=25\) और \(7^2=49\) हैं। / \(5^2=25\) and \(7^2=49\).
Step 2
Why this answer is correct
\(25\times49=1225\)। / \(25\times49=1225\).
Step 3
Exam Tip
वर्ग रूप में दोनों घातें 2 हैं, इसलिए गुणा साफ करें। / Both powers are 2 in this square form, so multiply carefully.
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किस संख्या का अभाज्य गुणनखंडन \(2\times3\times5\times7\times11\) है?
Which number has prime factorisation \(2\times3\times5\times7\times11\)?
#evaluate-factorisation
#number-2310
#easy
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A 2310
B 1155
C 4620
D 3300
Explanation opens after your attempt
Step 1
Concept
दिए गए सभी अभाज्य गुणनखंडों को गुणा करें। / Multiply all given prime factors.
Step 2
Why this answer is correct
\(2\times3\times5\times7\times11=2310\)। / \(2\times3\times5\times7\times11=2310\).
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 \(2^3\times3^2\times5^2\) है?
Which number has prime factorisation \(2^3\times3^2\times5^2\)?
#evaluate-factorisation
#number-1800
#easy
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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
घातों को पहले सरल करें, फिर गुणा करें। / Simplify powers first, 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
#easy
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A 1296
B 648
C 2592
D 1728
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\) और \(3^4=81\) निकालें। / Calculate \(2^4=16\) and \(3^4=81\).
Step 2
Why this answer is correct
\(16\times81=1296\)। / \(16\times81=1296\).
Step 3
Exam Tip
अभाज्य घातों का मान निकालकर गुणा करें। / Evaluate prime powers and then multiply.
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अभाज्य गुणनखंडन में घात लिखने का मुख्य लाभ क्या है?
What is the main benefit of writing powers in prime factorisation?
#prime-factorisation
#powers
#concept-check
#easy
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A दोहराए गए अभाज्य गुणनखंडों को छोटा और साफ लिखना / Writing repeated prime factors shortly and clearly
B संख्या को जोड़ में बदलना / Changing the number into addition
C संयुक्त गुणनखंड छिपाना / Hiding composite factors
D उत्तर को अनुमान से लिखना / Writing the answer by guess
Explanation opens after your attempt
Correct Answer
A. दोहराए गए अभाज्य गुणनखंडों को छोटा और साफ लिखना / Writing repeated prime factors shortly and clearly
Step 1
Concept
जब कोई अभाज्य संख्या बार-बार आती है, तो घात का उपयोग किया जाता है। / When a prime repeats, powers are used.
Step 2
Why this answer is correct
जैसे \(2\times2\times2\) को \(2^3\) लिखा जाता है। / For example, \(2\times2\times2\) is written as \(2^3\).
Step 3
Exam Tip
इससे उत्तर छोटा, साफ और परीक्षा में पढ़ने योग्य बनता है। / This makes the answer short, clear, and easy to read in exams.
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