Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.

89

To find – natural numbers between 102 and 998 divisible by 2 and 5 both

Property – for an A.P. with first term a and common difference d, n^th term is given by,

t_n = a + (n – 1)d

Answer –

The numbers which are divisible by both 2 and 5 will be the numbers which are divisible by

(2× 5) = 10.

Therefore, numbers between 102 and 998 which divisible by 10 are

110 ,120, 130, …………….990

The above sequence is an A.P. with first term a = 110 and common difference d = 10

And last term t_n = 990

t_n = a + (n – 1)d

∴ 990 = 110 + (n – 1) ×10

∴ 990 = 110 + 10n – 10

∴ 990 = 100 + 10n

∴ 10n = 890

∴ n = 89

Therefore, there are 89 natural numbers between 102 and 998 which are divisible by both 2 and 5.