Question

Find the smallest number by which the following number must be divided to obtain a perfect cube:
$81$

Answer 1

We have the given number as $81.$

$\begin{array}{cc}3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

Prime factors of $81=\underset{–}{3\times 3\times 3}\times 3$

Here one factor $3$ is not grouped in triplets.

Therefore $81$ must be divided by $3$ to make it a perfect cube.