Question

What is the smallest number with which 1188 should be divided to get a perfect cube?

Answer 1

$\begin{array}{cc}3& 1188\\ 3& 396\\ 3& 132\\ 2& 44\\ 2& 22\\ & 11\end{array}$

Prime factor of 1188 = 3 $\times$ 3 $\times$ 3 $\times$ 2 $\times$ 2 $\times$11

For perfect cube number the factors should be forming the triplet. Here 2 is forming the triplet but 2 and 11 does not.

That implies if we divide the given number by 44, the resultant will be perfect cube.
$\frac{1188}{44}$ = 27 = $3^3$