How many two-digit numbers are divisible by 3?

Ans. 30

Now before knowing the numbers divisible by three, you should know what numbers ‘divisible by 3 means’.

Whenever we divide a number by 3 and as a result, its remainder is a 0 this means that a number is divisible by 3.

For example: by dividing 27 by 3, we get the remainder as zero.

Divisibility Rule Of 3

The divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

Consider the number, 308. To check whether 308 is divisible by 3 or not, take the sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3, then the original number is also divisible by 3. Now, since 11 is not divisible by 3, 308 is also not divisible by 3.

Similarly, 729 is divisible by 3 completely as the sum of its digits i.e. 7+2+9=18, is a multiple of 3.

List Of Two Digits Numbers Divisible By 3

As you have probably figured out by now, the list of numbers divisible by 5 is infinite.

But there are only 30 two-digit numbers that are divisible by 3. They are as follows:

12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

Method To Find Out The Number Of Two-Digit Numerals Divided By 3

Two-digit numbers divisible by 3 are 12, 15, 18, 21…99

Here d= 3, therefore the sequence of AP

a= 12, tn=99

and common difference d= 3

tn= a+ (n-1)d

99= 12 + (n-1)3

87 =(n-1)3

n-1= 29

n= 30