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Divisibility Rules for numbers from 1 to 11

 Hi,

Today we are going to know about one of the interesting topics in maths that you would probably come across while doing tricky maths questions and it is divisibility Rules for numbers. If you have good command over divisibility Rules you can surely save yourself from doing rigorous calculation and Also ,it will be an addition to your question solving approach.

what are the divisibility rules

In this article we are going to cover all the rules from number 1 to 11 with easy understandable examples.

Divisibility Rules from number 1 to 11

The divisibility Rules are as follows:

Divisibility by Number 1: All numbers are divisible by 1 

Divisibility by Number Number 2:  A number is divisible by 2 if it has any of the following number 0,2,4,6,8 as unit digit.

Example : 
784 is completely divisible by 2
2230 is completely divisible by 2
53562 is completely divisible by 2
136566 is completely divisible by 2
4390748 is completely divisible by 2 

Divisibility by Number 3 : A number is completely divisible by 3 if the sum of its all digits is also divisible by 3.

Example :
63 is completely divisible by 3 
345 is completely divisible by 3 
4566 is completely divisible by 3 
86424 is completely divisible by 3 
399852 is completely divisible by 3 

Divisibility by Number 4 : A number is divisible by 4 if the number formed by its last two digits be completely divisible by 4.

Example :
016 is completely divisible by 4
2904 is completely divisible by 4 
56224 is completely divisible by 4 
657864 is completely divisible by 4 
1000484 is completely divisible by 4 

Divisibility by Number 5 : A number is divisible by 5 if its last digit is either 0 or 5.

Example 
450 is completely divisible by 5
2355 is completely divisible by 5

Divisibility by Number 6 : A number is divisible by 6 if it is divisible by both 2 and 3. Or A number is divisible by 6 if its prime factorization contains at least one pair of 2×3.

Example 
108 is completely divisible by 6
1002 is completely divisible by 6
99996 is completely divisible by 6
1000014 is completely divisible by 6 

Divisibility by Number 7 :  A number is divisible by 7 if the difference between twice of unit digit of  given number and remaining part of  the same number is either 0 or a multiple of 7.

Example
147 is divisible by 7 
Unit digit of 147 = 7 
2×7 =14 
14-14 =0

1526 is divisible by 7 
Unit digit of 1526 = 6 
6×2 = 12
152-12 = 140
140 is completely divisible by 7

Divisibility by Number 8 : A number is divisible by 8 if the number formed by its last three digits is a multiple of 8 or completely divisible by 8.

Example
8824 is completely divisible by 8
10028 is completely divisible by 8
45096 is completely divisible by 8 
100488 is completely divisible by 8 

Divisibility by Number 9 : A number is completely divisible by 9 if the sum of all its digits is divisible by 9.

Example
657 is completely divisible by 9
2799 is completely divisible by 9
875088 is completely divisible by 9 

Divisibility by Number 10: A number is divisible by 10 if it has 0 as its unit digit.

Example
760 is completely divisible by 10
900080 is completely divisible by 10
7600 is completely divisible by 10

Divisibility by Number 11: A number is completely divisible by 11 if the difference between the sum of digits at odd positions and  sum of digits at even places is either 0 or a multiple of 11.

Example
743655 is completely divisible by 11
1001 is completely divisible by 11
5654 is completely divisible by 11

Divisibility by Number 12 :

A number is divisible by 12 if it is divisible by both 3 and 4.

Example 
48 is divisible by both 3 and 4 hence it must be divisible by 12.
108 is divisible by both hence divisible by 12 also

Divisibility by Number 15: A number is divisible by 15 if it is divisible by Both 3 and 5.

Example 
225 is divisible by 15 as it is divisible by 3 and 5 both.
15225 is divisible by 15 as it is divisible by Both 3 and 5.

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