Question

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

$81$

Answer 1

The given number is $81$

Prime factorizing $81$, we get,

$81=3\times 3\times 3\times 3=3^4$.

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

Here, number of $3$'s is $4$.

So we need to divide the factorization by $3$ to make $81$ a perfect cube.

Hence, the smallest number by which $81$ must be divided to obtain a perfect cube is $3$.