Question

Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.

Answer 1

Factorising 2560 into prime factors.

2560=$\overline{2\times 2\times 2}\times \overline{2\times 2\times 2}\times \overline{2\times 2\times 2}\times 5$
Making them in groups of 3 equal factors, we are left 5
$\therefore$ To make it into a group of 3, we have to multiply it by $5\times 5$ i.e. by 25.
Hence, the smallest number by which it is multiplied = 25