10 Easy Divisibility Rules for Numbers with Examples

Mathematics

Divisibility Rules for Numbers with Examples will make you understand the concept easily and clearly. Divisibility is one of the important concepts in mathematics and it is frequently used in competitive exam papers. If we learn and follow some simple rules, we can easily check the divisibility of any number by other numbers.

Divisibility Rules for Numbers with Examples
Image by Clker-Free-Vector-Images from Pixabay 

Divisibility Rules for Numbers with Examples

Divisibility by 2:
If the unit digit is even then the number is divisible by 2.

Example:
45126 has an even last digit, so it is divisible by 2.
785463 has an odd last digit, it is not divisible by 2.

Divisibility by 3:
If the sum of the digits is divisible by 3 then the number is also divisible by 3.
Example:
In 45656265, the sum of digits is (4+5+6+5+6+2+6+5=39) and 39 is divisible by 3, so the number is also divisible by 3.

Divisibility by 4:

If the last 2-digits are divisible by 4 then the number is also divisible by 4.

Example:
In 45568, the last 2-digits are 68, and 68 is divisible (68/4=17) by 4. So the number is also divisible by 4.

Divisibility by 5:
If the last digit is 5 or 0 then the number is divisible by 5.

Example:
The number 123456 is not divisible by 5 as the last digit is not 5 or 0.

Divisibility by 6:
If the number is divisible by both 2 and 3 then it is also divisible by 6.

Divisibility by 7:
Step 1: Take out the last digit of the number and double it.
Step 2: Subtract the double of the last digit (2L) from the remaining digit number (R).
Step 3: If the result (R-2L) is either 0 or divisible by 7, then the original number is also divisible by 7.
If (R-2L) is still a big number then repeat the steps.

Example:
Number = 452784

Last digit (L) = 4
Remaining number (R) = 45278
(R-2L) = 45278 – 8 = 45270

Repeating the steps, (R-2L) = 4527-0=4527
Repeating the steps, (R-2L) = 452-14=438
Repeating the steps, (43-16)=27

Clearly, 27 is not divisible by 7. So the original number is also not divisible by 7.

Divisibility by 8:
If the last 3-digits are divisible by 8 then the number is also divisible by 8.
Example:
Number = 654720
Last 3-digits = 720
The last 3-digits are clearly divisible by 8. So the original number is also divisible by 8.
Divisibility by 9:
If the sum of the digits is divisible by 9 then the number is also divisible by 9.

Example:
Number = 789453
Sum of the digits = 7+8+9+4+5+3 = 36

The sum (36) is divisible by 9. So the original number is also divisible by 9.
Divisibility by 10:
If the unit digit of the number is 0 then it is divisible by 10.

Example:
Number = 987456
The last digit of the number is not 0. So the number is not divisible by 10.

Divisibility by 11:
Step 1: Find the sum of the digits at odd places. (∑digits at odd places)
Step 2: Find the sum of the digits at even places. (∑digits at even places)
Step 3: If the difference, ( ∑digits at odd places – ∑digits at odd places ) is either 0 or divisible by 11 then the original number is also divisible by 11.

Example:
Number = 987054321
Sum of digits at odd places = 9+7+5+3+1 = 25
Sum of digits at even places = 8+0+4+2 = 14
Difference = 25-14 = 11

The difference is divisible by 11. So the original number is also divisible by 11.

You are reading Divisibility Rules for Numbers with Examples.
Divisibility by 12:
If the number is divisible by 3 and 4 then it is also divisible by 12.
Divisibility by 13:
Step 1: Take out the last digit and multiply it by 4. (4L)
Step 2: Add the result (4L) to the remaining digit number (R).
Step 3: If the result (R+4L) is either 0 or divisible by 13 then the original number is also divisible by 13.
If (R+4L) is still a big number then repeat the steps.

Example:
Number = 988676
Last digit = 6
Remaining Number = 98867
(R+4L) = 98867 + 4 x 6 = 98891

Repeating the steps, (R+4L) = 9889 + 4 x 1 = 9893
Repeating the steps, (R+4L) = 989 + 4 x 3 = 1001
Repeating the steps, (R+4L) = 100 + 4 x 1 =104

104 is divisible by 13. So the original number is also divisible by 13.

Divisibility by 14:
If the number is divisible by 2 and 7 then it is also divisible by 14.
Divisibility by 15:
If the number is divisible by 3 and 5 then it is also divisible by 15.
Divisibility by 16:
If the last 4-digits are divisible by 16 then the number is also divisible by 16.
Example:
Number = 4567816
Last 4-digits = 7816
7816 is not divisible by 16. So the original number is also not divisible by 16.

Divisibility Rules for Numbers with Examples. Also, read about the Basics of Numbers.