Question

Find the smallest number by which the following number must be divided to obtain a perfect cube: $128$

Answer 1

Calculate the prime factorisation of $128$.

$128=2\times 2\times 2\times 2\times 2\times 2\times 2$

To make it a perfect cube, it should be divided by $2$.

$\begin{array}{rcl}\frac{128}{2}& =& \frac{2\times 2\times 2\times 2\times 2\times 2\times 2}{2}\\ & =& 2\times 2\times 2\times 2\times 2\times 2\end{array}$

which is a perfect cube of $4$.

Hence, smallest number by which $128$ must be divided to obtain a perfect cube is $2$.