Question

Find the smallest number by which the following number must be divided to obtain a perfect cube:

$128$

Answer 1

Prime factorising $128$, we get,

$128=2\times 2\times 2\times 2\times 2\times 2\times 2=2^7$.

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

Here, number of $2$'s is $7$.

So we need to divide the factorization by $2$ to make $128$ a perfect cube.

Hence, the smallest number by which $128$ must be divided to obtain a perfect cube is $2$.