Question

By which smallest number $8788$ must be divided so that quotient is a perfect cube

Answer 1

The given number is $8788$

The prime factorisation of $8788$ is given by,

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

We see that prime factor $2$ does not occur in the group of $3$, hence the given number is not a perfect cube.

In order to make it a perfect cube, it must be divided by $4$.

Now, $\frac{8788}{4}=\frac{2\times 2\times 13\times 13\times 13}{4}$

$\Rightarrow 2197=13\times 13\times 13$, which is a perfect cube number.

Thus, the cube root of $2197=13$