Question

What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?

Answer 1

Factorising 1600 into prime factors
$1600=\overline{2\times 2\times 2}\times \overline{2\times 2\times 2}\times 5\times 5$
Making them in groups of 3 equal factors.
We are left with $5\times 5$
$\therefore 5\times 5$ i.e., 25 is to be divided.

Hence, least number to be divided for getting perfect cube = 25