Question

Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.

Answer 1

2560

2560 can be expressed as the product of prime factors in the following manner:


2560 = $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5$

To make this a perfect square, we have to multiply it by 5$\times$5.
Therefore, 2560 should be multiplied by 25 so that the product is a perfect cube.