how many two digit numbers are divisible by 3

Two-digit numbers range from 10 to 99. To find how many two-digit numbers are divisible by 3, identify the first and last two-digit multiples of 3.

First two-digit number divisible by 3:
12 ÷ 3 = 4
So, 12 is the first multiple.

Last two-digit number divisible by 3:
99 ÷ 3 = 33
So, 99 is the last multiple.

Using the arithmetic progression formula:

Number of terms = [(Last − First) ÷ Common Difference] + 1

= [(99 − 12) ÷ 3] + 1
= 87 ÷ 3 + 1
= 29 + 1
= 30

Therefore, there are 30 two-digit numbers divisible by 3.

In conclusion, the total number of two-digit numbers divisible by 3 is 30.