How many natural numbers are there between 23 and 100 which are exactly divisible by 6?

Required numbers are 24, 30, 36, 42, ..., 96

This is an A.P. in which a = 24, d = 6 and l = 96

Let the number of terms in it be n.

Then t_n = 96  ⟹  a + (n - 1)d = 96

⟹ 24 + (n - 1) x 6 = 96

⟹ (n - 1) x 6 = 72

⟹ (n - 1) = 12

⟹ n = 13

Required number of numbers = 13.