How many three-digit numbers are divisible by 7?

Since, 100 is the smallest three digit number and it gives a reminder of 2 when divided by 7, therefore, 105 is the smallest three digit number which is divisible by 7.

Since, 999 is greatest three digit number, and it gives a reminder of 5, thus 999 – 5 = 994 will be the greatest three digit number which is divisible by 7.

Therefore, here we have,

First term (a) = 105,

The last term (a_n) = 994

The common difference = 7

We know that, a_n = a + (n – 1)d

Or, 994 = 105 + (n – 1)7

Or, (n – 1)7 = 994 – 105 = 889

Or, n – 1 = 127

Or, n = 128

Thus, there are 128 three digit numbers which are divisible by 7.