Question

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

Answer 1

Step 1. Find the prime factors

Given number, $256$

$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Step 2. Find the smallest number multiplied to obtain perfect cube

By assorting the factors in triplets of equal factors, $256=(2\times 2\times 2)\times (2\times 2\times 2)\times 2\times 2$

Here, $2$ cannot be arranged into triplets of equal factors.

$\therefore$ We will multiply $256$ by $2$ to get a perfect cube.

Hence, the smallest number by which $256$ must be multiplied to obtain a perfect cube is $2$.