Question

Find the smallest number by which 1575 must be divided so that the quotient becomes a perfect square.

Answer 1

Given number is 1575 first we write it as the product of prime factors

3	1575
3	525
5	175
5	35
7	7
	1

$\therefore$ $1575=\underset{–}{3\times 3}\times \underset{–}{5\times 5}\times 7$
Clearly 7 has no pair so if we divide it by 7 then quotient become a perfect square