Question

Find the smallest number by which the given number must be divided so that the resulting number is a perfect square: 

2904

Answer 1

For  question, factorise the number into its prime factor.

2904 = 2 x 2 x 2 x 3 x 11 x 11 

Grouping the factors into pairs:
2904 = (2 x 2) x (11 x 11) x 2 x 3
Here, the factors 2 and 3 do not occur in pairs. To be a perfect square, all the factors have to be in pairs. Hence, the smallest number by which 2904 must be divided for it to be a perfect square is 2 x 3, i.e. 6.