Question

Numbers given below are not perfect squares. Use prime factorization method to find the smallest number by which these can be divided to make them perfect squares.

(i) 1000
(ii) 867
(iii) 4375

Answer 1

(i) 1000

∴ 1000 = 2 x 2 x 2 x 5 x 5 x 5

= 2 x 2 x 5 x 5 x 10

10 has no pair.

So 10 is required to divide.

(ii) 867

∴ 867 = 3 x 17 x 17

(iii) 4375

∴ 4375 = 5 x 5 x 5 x 5 x 7

∵ 7 has no pair

∴ 7 is required to divide