Question

Find the smallest number by which $256$ must be multiplied to obtain a perfect cube.

Answer 1

By prime factorization, $256$ can be written as $2^3\times 2^3\times 2^2$ by making $2$ into groups of $3.$

In the third group, one $2$ is missing.

$256=2^3\times 2^3\times 2^2$

So, $512=2^3\times 2^3\times 2^2\times 2$

Hence, number $2$ must be smallest number that must be multiplied to make it a perfect cube.