NUMBER OF 3 DIGIT NUMBERS DIVISIBLE BY 11

First let us see, how to find the number of numbers from 1 to 100 which are divisible by 11.

Step 1 :

Divide 100 by 11.

= ¹⁰⁰⁄₁₁

= 9.09.09.....

Step 2 :

When we divide 100 by 11, we get about 9.09.

We should not round this result to the nearest integer (that is 10 or 9).

We have to consider the largest integer contained in 9.09.

That is 9.

From 1 to 100, number of numbers divisible by 11 is 9.

Be careful!

The above method will work only, if you take the numbers from 1. In other words, the above method will work for the first n natural numbers.

How many three digit numbers  are divisible by 11?

Step 1 :

The smallest three digit number = 100

The largest three digit number = 999

Step 2 :

From 1 to 999, find the number of numbers, which are divisible by 11.

Divide 999 by 11.

= ⁹⁹⁹⁄₁₁

≈ 90.82

From 1 to 999, number of numbers divisible by 11 is 90.

Step 3 :

From 1 to 99, find the number of numbers, which are divisible by 11.

Divide 99 by 11.

= ⁹⁹⁄₁₁

= 9

From 1 to 99, number of numbers divisible by 11 is 9.

Step 4 :

Number of numbers divisible by 11 (1 to 999) = 90

Number of numbers divisible by 11 (1 to 99) = 9

Number of numbers divisible by 11 (100 to 999) :

= 90 - 9

= 81

Therefore, number of three digit numbers (100 to 999) which are divisible by 11 is 81.

In the same way, we can find the number of three-digit numbers which are divisible by any number.

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