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

Given data

• Count multiples of 6 strictly between 23 and 100 (i.e., > 23 and < 100).

Concept / Approach

• Number of multiples of m in (A, B) equals \u230a(B − 1)/m\u230b − \u230aA/m\u230b, or equivalently \u230aB/m\u230b − \u230aA/m\u230b when B is excluded.

Step-by-step calculation

First multiple > 23 is 24; last multiple < 100 is 96.Count = \u230a99/6\u230b − \u230a23/6\u230b = 16 − 3 = 13(List: 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96)

Common pitfalls

• Including 100 if interpreting "between" as inclusive; here, 100 is excluded and 96 is the last valid multiple.

Final Answer

13