Question

Find the smallest number by which $8788$ must be multiplied to obtain a perfect cube.

Answer 1

Prime factorising $8788$, we get,

$8788=2\times 2\times 13\times 13\times 13$

$=2^2\times {13}^3$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.

Here, number of $2$'s is $2$ and number of $13$'s is $3$.

So we need to multiply another $2$ to the factorization to make $8788$ a perfect cube.

Hence, the smallest number by which $8788$ must be multiplied to obtain a perfect cube is $2$.