Question

Find the smallest number which should be multiplied to $432$ to get a perfect cube.

Answer 1

Prime factorising $432$, we get,

$432=2\times 2\times 2\times 2\times 3\times 3\times 3$

$=2^4\times 3^3$.

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

Here, number of $2$'s is $4$ and number of $3$'s is $3$.

So we need to multiply another $2^2$ in the factorization to make $432$ a perfect cube.

Hence, the smallest number by which $432$ must be multiplied to obtain a perfect cube is $2^2=4$.