Question

Is $53240$ a perfect cube? If not then by which smallest natural numbers should be divided so that the quotient is a perfect cube?

Answer 1

Prime factorising, $53240=5\times 2^3\times {11}^3$.

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

The prime factor $5$ does not appear in triplet form.

Therefore, $53240$ is not a perfect cube.

Since in the factorization, $5$ appears only one time, we must divide the number $53240$ by $5$, then the quotient is a perfect cube.

$\therefore 53240÷5=10648$

$=22\times 22\times 22={22}^3$, which is a perfect cube.

$\therefore$ The smallest number by which $53240$ should be divided to make it a perfect cube is $5$.