Question

Find the smallest number by which $33275$ must be multiplied so that the product is a perfect cube.

Answer 1

On prime factorization of $33275$, we get,

$33275=5\times 5\times 11\times 11\times 11$

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

A perfect cube has factors with exponents $3.$

Here, number of $5$'s is $2$ and number of $11$'s is $3$.

So, we need to multiply another $5$ to the number $33275$ to make it a perfect cube.

Hence, the smallest number by which $33275$ must be multiplied to obtain a perfect cube is $5.$