Question

Is the following number a perfect cube or not? If it is perfect cube then answer $1$, otherwise answer $0$.

$106480$

Answer 1

Prime factorising, we get,

$106480=2\times 2\times 2\times 2\times 5\times 11\times 11\times 11$

$=(2^3\times 2\times 5\times {11}^3)={(2\times 11)}^3\times 2\times 5$

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

In the above factorisation, $2$ and $5$ does not have their powers as multiple of $3$.

Therefore, $106480$ is not a perfect cube.

Hence, $0$ is the answer.