Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube: $675$

Answer 1

Step 1. Finding the prime factors:

Given number, $675$

$675=3\times 3\times 3\times 5\times 5$

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

By assorting the factors in triplets of equal factors, $675=(3\times 3\times 3)\times 5\times 5$

Here, $5$ cannot be arranged into triplets of equal factors.

$\therefore$ We will multiply $675$ by $5$ to get a perfect cube.

Hence, the smallest number by which $675$ must be multiplied to obtain a perfect cube is $5$.