How many three digit numbers are divisible by 87?

Three digit numbers divisible by 87 are,

174, 261, ………, 957.

The above series is an A.P. with a = 174 and d = 261 - 174 = 87 and last term = 957.

Let no. of terms in the A.P. be n.

∴ a_n = 957

⇒ a + (n - 1)d = 957

⇒ 174 + (n - 1)(87) = 957

⇒ 174 + 87n - 87 = 957

⇒ 87n + 87 = 957

⇒ 87n = 957 - 87

⇒ 87n = 870

⇒ n = 10.

Hence, there are 10 three digit numbers which are divisible by 87.