HOW MANY 3 DIGIT NUMBERS ARE DIVISIBLE BY 6 IN ALL ?

About the topic "How many 3 digit numbers are divisible by 6 in all ?"

"How many 3 digit numbers are divisible by 6 in all ?" is a difficult question having had by the students who study math to get prepared for competitive exams. 

For some students, getting answer for the above question 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 6,  how will you find?

Answer :

Step 1 :

                                             Divide 100 by 6.

100/6  =  16.67

Step 2 :

When we divide 100 by 6, we get 16.67

We should not round this result to the nearest integer. (That is 16 or 17).

We have to consider the largest integer contained in 16.67

That is "16"

From 1 to 100, number of numbers divisible by 6 is 16.

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 3 digit numbers are divisible by 6 in all?

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 6 from 1 to 999

Divide 999 by 6 --------------> 999/6 = 166.5

Therefore number of numbers divisible by 6 from 1 to 999 = 166

Step 3 :

Let us find number of numbers divisible by 6 from 1 to 99

Divide 99 by 6 --------------> 99/6 = 16.5

Therefore number of numbers divisible by 6 from 1 to 99 = 16

Step 4 :

Number of numbers divisible by 6 (1 to 999) = 166

Number of numbers divisible by 6 (1 to 99) = 16

Number of numbers divisible by 6 (100 to 999)

                                            = 166 - 16

                                            =  150    

Therefore, number of three digit numbers (100 to 999) which are divisible by 6 is 150.

This is how to we have to find number of 3 digit numbers divisible by 6

The concept explained in the above problem will not only be helpful to get answer for the question "How many 3 digit numbers are divisible by 6 in all ?" , 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 many 3 digit numbers are divisible by 6 in all ?".

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