Question

Find the smallest number by which $8788$ must be divided so that the quotient is a perfect cube.

Answer 1

Calculate the prime factorization of $8788$.

Given number is $8788$.

$8788=\left(2\times 2\right)\times \left(13\times 13\times 13\right)$

To make it triplet, it needs to be divided by $2\times 2=4$ to have that all factors be triplets.

So, required number

$\begin{array}{rcl}\frac{8788}{4}& =& \frac{\left(2\times 2\right)\times \left(13\times 13\times 13\right)}{4}\\ & =& 13\times 13\times 13\\ & =& 2197\end{array}$

Hence, the smallest number by which $8788$ must be divided so that the quotient is a perfect cube is $4$.