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The least number by which 12348 must be divided so as to have the quotient as a perfect square.
- a)6
- b)7
- c)4
- d)9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The least number by which 12348 must be divided so as to have the quot...
12348 ← even number, you can divide it by 2
= 2 * 6174 ← even number, you can divide it by 2
= 2 * 2 * 3087 ← the sum is (3 + 0 + 8 + 7) = 18 ← 18 is divisible by 3 ← you can divide it by 3
= 2 * 2 * 3 * 1029 ← the sum is (1 + 0 + 2 + 9) = 12 ← 12 is divisible by 3 ← you can divide it by 3
= 2 * 2 * 3 * 3 * 343 ← you know that 343 is divisible by 7
= 2 * 2 * 3 * 3 * 7 * 49 ← recall: 49 = 7^2
= 2 * 2 * 3 * 3 * 7 * 7^2
= 2^2 * 3^2 * 7^2 * 7
= (2 * 3 * 7)2 * 7
= 42^2 * 7 ← the number is 7 → 12348/7 = 42^2 ← this is the perfect square
Most Upvoted Answer
The least number by which 12348 must be divided so as to have the quot...
Given number: 12348
To find: The least number by which 12348 must be divided so as to have the quotient as a perfect square.
Approach:
- Find the prime factors of the given number 12348.
- Find the power of each prime factor.
- The least number by which 12348 must be divided so as to have the quotient as a perfect square is the product of all prime factors raised to the power of the next multiple of 2.
Prime factorization of 12348:
- 2 × 2 × 3 × 13 × 79
Power of each prime factor:
- 2^2 × 3^1 × 13^1 × 79^1
To make the quotient a perfect square, we need to raise each prime factor to the power of the next multiple of 2.
- 2^2 × 3^2 × 13^2 × 79^2
Therefore, the least number by which 12348 must be divided so as to have the quotient as a perfect square is:
- 2^2 × 3^2 × 13^2 × 79^2 = 281540836.
Hence, the correct option is (B) 7.
To find: The least number by which 12348 must be divided so as to have the quotient as a perfect square.
Approach:
- Find the prime factors of the given number 12348.
- Find the power of each prime factor.
- The least number by which 12348 must be divided so as to have the quotient as a perfect square is the product of all prime factors raised to the power of the next multiple of 2.
Prime factorization of 12348:
- 2 × 2 × 3 × 13 × 79
Power of each prime factor:
- 2^2 × 3^1 × 13^1 × 79^1
To make the quotient a perfect square, we need to raise each prime factor to the power of the next multiple of 2.
- 2^2 × 3^2 × 13^2 × 79^2
Therefore, the least number by which 12348 must be divided so as to have the quotient as a perfect square is:
- 2^2 × 3^2 × 13^2 × 79^2 = 281540836.
Hence, the correct option is (B) 7.
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The least number by which 12348 must be divided so as to have the quotient as a perfect square.a)6b)7c)4d)9Correct answer is option 'B'. Can you explain this answer?
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The least number by which 12348 must be divided so as to have the quotient as a perfect square.a)6b)7c)4d)9Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The least number by which 12348 must be divided so as to have the quotient as a perfect square.a)6b)7c)4d)9Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The least number by which 12348 must be divided so as to have the quotient as a perfect square.a)6b)7c)4d)9Correct answer is option 'B'. Can you explain this answer?.
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