Question

Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.

Answer 1

The prime factor of 8768 are

$\begin{array}{cc}\text{2}& 8768\\ 2& 4384\\ 2& 2192\\ 2& 1096\\ 2& 548\\ 2& 274\\ 137& 137\\ & 1\end{array}$

$=2\times 2\times 2\times 2\times 2\times 2\times 137=(2\times 2\times 2)\times (2\times 2\times 2)\times 137$

For perfect cube, prime factor should form triplet.

Here, we can see all 2's are forming a triplet, but 137 does not.

Clearly, 8768 must be divided by 137, to make it a perfect cube.

After dividing by 137, we get 64 as a quotient, which is a perfect cube.