Question

Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?

Answer 1

The prime factor of 77175 are

$=3\times 3\times 5\times 5\times 7\times 7\times 7=(7\times 7\times 7\times )\times 3\times 3\times 5\times 5$

Clearly,77175 must be multiplied by $3\times 5=15$.