Question

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

$135$

Answer 1

Prime factorising $135$, we get,

$135=5\times 3\times 3\times 3$ $=3^3\times 5^1$.

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

Here, number of $3$'s is $3$ and number of $5$'s is $1$.

So we need to divide the factorization by $5$ to make $135$ a perfect cube.

Hence, the smallest number by which $135$ must be divided to obtain a perfect cube is $5$.