Question

Find the smallest number by which 26244 should be divided so that the quotient is a perfect cube.

Answer 1

The prime factors of 26244 are

$2\times 2\times 3\times 3\times 3\times 3\times 3\times 3\times 3\times 3=(3\times 3\times 3)\times (3\times 3\times 3)\times 3\times 3\times 2\times 2$

Clearly,26244 must be divided by $3\times 3\times 2\times 2=36$