Question

The smallest number that is to be multiplied with 6655 so that the product will be a perfect cube is ___.

Answer 1

$\begin{array}{cc}11& 6655\\ 11& 605\\ 11& 55\\ & 5\end{array}$

Prime factors of 6655 = 11 $\times$ 11 $\times$ 11 $\times$ 5
To make it a perfect cube, the factors should appear in sets of 3.
So, if we multiply 5 $\times$ 5 (i.e. 25) with 6655, the product will be a perfect cube.