Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube:
$100$

Answer 1

We have the number $100$

Prime factors of $100=2\times 2\times 5\times 5$

Here factor $2$ and $5$ both do not appear in 3’s group.

Therefore 100 must be multiplied by $2\times 5=10$ to make it a perfect cube.

$\begin{array}{cc}2& 100\\ 2& 50\\ 5& 25\\ 5& 5\\ & 1\end{array}$