What is the smallest number by which 392 must be multiplied so that the product is a perfect cube?

By Team Aakash Byju's | 23rd January 2023

The correct answer is 7.

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A number can be said to be perfect if all its prime factors can be cubed. So, to check if 392 is a perfect cube or not, let us find its prime factors.

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392 = (2×2×2) × (7×7)

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Since each prime factor must have a power of 3 to make the given number a perfect cube.

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we need to multiply 392 by 7.

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What is the smallest number by which 392 must be multiplied so that the product is a perfect cube?

The correct answer is 7.

Brief Explanation

A number can be said to be perfect if all its prime factors can be cubed. So, to check if 392 is a perfect cube or not, let us find its prime factors.

392 = (2×2×2) × (7×7)

=> 392 = (2) × (7)

3

2

Since each prime factor must have a power of 3 to make the given number a perfect cube.

we need to multiply 392 by 7.

Thus, multiplying 392 by 7 results in a number that is a perfect cube.

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