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What is the smallest number by which 2304 may be divided so that the quotient is a perfect cube?

User Arok
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2 Answers

4 votes

solution: 16

how to answer

User Cerlin
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3 votes

Answer:

16

Explanation:

To find the smallest number by which 2304 can be divided so that the quotient is a perfect cube, we need to identify the highest power of each prime factor that can be divided.

The prime factorization of 2304 is:

2304 = 2^7 * 3^2

To make the quotient a perfect cube, we need to divide by the highest power of 2 and 3 that would result in a perfect cube.

The highest power of 2 that can be divided is 2^6 (64), and the highest power of 3 that can be divided is 3^2 (9).

Therefore, the smallest number by which 2304 can be divided so that the quotient is a perfect cube is 64 * 9 = 576.

User Osama F Elias
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