NUMBER OF 3 DIGIT NUMBERS DIVISIBLE BY 11

About the topic "Number of 3 digit numbers divisible by 11"

"Number of 3 digit numbers divisible by 11", "How many three digit numbers  are divisible by 11?" are all difficult questions having had by the students who study math to get prepared for competitive exams. 

For some students, getting answer for the above questions is never being easy and always it is a challenging one.

Basic Concept

From 1 to 100, if you want to find number of numbers which are divisible by 11,  how will you find?

Answer :

Step 1 :

                                             Divide 100 by 11.

100/11  =  9.09

Step 2 :

When we divide 100 by 7, we get 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 mentioned method will work only if you take the numbers from 1.

Important Note:

Whenever we want to find number of numbers which are divisible by "k" from 1 to a particular number "x", we have to divide "x" by "k".

To get the number of numbers divisible by "k" from 1 to "x", we have to consider the largest integer contained in the result of "x/k"

(In the result of "x/k", we should not round to the nearest integer. For example, we should not round 14.9 to 15 or 14.1 to 14)

How many three digit numbers  are divisible by 11?

Solution:

Step 1 :

The smallest three digit number = 100

The largest three digit number = 999

Step 2 :

Let us find number of numbers divisible by 11 from 1 to 999

Divide 999 by 11 --------------> 999/11 = 90.82

Therefore number of numbers divisible by 11 from 1 to 999 = 90

Step 3 :

Let us find number of numbers divisible by 11 from 1 to 99

Divide 99 by 11 --------------> 99/11 = 9

Therefore number of numbers divisible by 11 from 1 to 99 = 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.

This is how to we have to find number of 3 digit numbers divisible by 11

The concept explained in the above problem will not only be helpful to find number of 3 digit numbers divisible by 11, it can also be applied to find number of 3 digit numbers which are divisible by any number.   

We hope, the problem explained above would be much helpful to the students who has difficulty with the question "How to find number of 3 digit numbers divisible by 11?".

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