Question

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

Answer 1

Calculate the prime factorisation of $81$.

$81=3\times 3\times 3\times 3$

To make it a perfect cube, it should be divided by $3$.

$\begin{array}{rcl}\frac{81}{3}& =& \frac{3\times 3\times 3\times 3}{3}\\ & =& 3\times 3\times 3\\ & =& 27\end{array}$

which is a perfect cube of $3$.

Hence, the smallest number by which $81$ must be divided to obtain a perfect cube is $3$.