Question

Find the smallest number by which 100 should be multiplied to obtain a perfect cube.

Answer 1

Factorising 100 using the prime factorisation method,

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

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.