Question

Find the smallest number by which $1323$ must be multiplied so that the product is a perfect cube.

Answer 1

Factorising $1323$ into prime factors, $1323=\overline{3\times 3\times 3}\times 7\times 7$
Making them in groups of 3 equal factors we see that $7\times 7$ are left.

$\therefore$ To make it into a group of $3$, we have to multiply it by $7$
Hence the smallest number by which it is multiplied $=7$