Question

For the non- perfect cube $243$, find the smallest number by which it must be
$\left(ii\right)$Divided so that the quotient is a perfect cube

Answer 1

Find the smallest number

Prime factors of $243$:
$243=3\times 3\times 3\times 3\times 3$

On grouping the factors of $243$, we get
$243=\{3\times 3\times 3\}\times 3\times 3$

Clearly, on grouping the factors in triplts of equal factors, we are left with two factors i.e., $3\times 3$

Thus, we need to divide $243$ by $3\times 3=9$ to make the quotient a perfect cube.

Hence, the smallest required number is $9$.