# How many two-digit numbers are divisible by 3?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

There are a total 30 two-digit numbers that are divisible by 3. Candidates can find the answer easily through Arithmetic Progression. To determine the total two-digit numbers are divisible by 3 we have to use the concept of AP and use the nth term of the AP formula. The AP formula is:

an= a1+(n−1)d

We already know that the first two digit number divisible by three is 12 and the last two digit number divisible by three is 99. So, the list of two digit numbers that are divisible by 3 is as follows

12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42,……….. 99

Now, we will use the AP formula: an= a1+(n−1)d

Here a1 = 12, d = 3, an = 99. We have to find the value of ‘n’.

By putting the above-mentioned values in the formula, we will get the following equation

99 = 12 + (n−1)3

99 = 12 + 3n – 3

99 = 12 – 3 + 3n

99 = 9 + 3n

99 – 9 = 3n

3n = 90

n = 90 ÷ 3

n = 30

Here the value of n = 30, hence the total two-digit numbers that are divisible by 3 is 30.

Table of content

## Total Two-Digit Numbers Divisible by 3

There are 30 two-digit numbers in all that are divisible by three. Through Arithmetic Progression, candidates can quickly determine the solution.

Arithmetic Progression also known as AP is a progression or sequence of numbers that keeps the difference between any succeeding term and its preceding term constant throughout the entire sequence. In that AP, the constant difference is known as the common difference.

A good example of an arithmetic progression (AP) is the sequence 3, 6, 9, 12, 15….. which follows a pattern in which each number is obtained by adding 3 to the previous term.

Summary:

## How many two-digit numbers are divisible by 3?

Total 30 two-digit numbers are divisible by 3. This can be calculated by using the concept of AP wherein we have to use the formula of AP i.e. an= a1+(n−1)d. Using this formula one can easily find the total two-digit numbers that are divisible by 3.

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