Question

How many three-digit numbers are divisible by 87?

Answer 1

The three-digit numbers divisible by 87 are as follows.

174, 261, ....., 957

Clearly, this forms an A.P. with the first term a = 174 and common difference d = 87.

Last term = n^th term = 957

The general term of an A.P. is given by

t_n = a + (n – 1)d

`=>` 957 = 174 + (n – 1)(87)

`=>` 783 = (n – 1) × 87

`=>` 9 = n – 1

`=>` n = 10

Thus, 10 three-digit numbers are divisible by 87.