Question

Find the smallest number by which the following number must be divided to obtain a perfect cube: $704$

Answer 1

Calculate the prime factorisation of $704$.

$704=2\times 2\times 2\times 2\times 2\times 2\times 11$

To make it a perfect cube, it should be divided by $11$.

$\begin{array}{rcl}\frac{704}{11}& =& \frac{2\times 2\times 2\times 2\times 2\times 2\times 11}{11}\\ & =& 2\times 2\times 2\times 2\times 2\times 2\\ & =& 4^3\\ & =& 64\end{array}$

which is a perfect cube of $4$.

Hence, the smallest number by which $704$ must be divided to obtain a perfect cube is $11$.