Question

Find the smallest number by which the following number must be divided to obtain a perfect cube: $135$.

Answer 1

Calculate the prime factorisation of $135$.

$135=3\times 3\times 3\times 5$

To make it a perfect cube, it should be divided by $5$ so that the factors can be grouped into triplets.

$\begin{array}{rcl}& \Rightarrow & \frac{135}{5}=\frac{3\times 3\times 3\times 5}{5}\\ & =& 3\times 3\times 3\\ & =& 27\end{array}$

which is a perfect cube of $3$.

Hence, the smallest number by which $135$ must be divided to obtain a perfect cube is $5$