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

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.

If the sum of the digits is divisible by 3 then the number is also divisible by 3.

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:

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.

Example:

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

Example:

Number = 452784

Remaining number (R) = 45278

(R-2L) = 45278 – 8 = 45270

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.

Number = 654720

Last 3-digits = 720

The last 3-digits are clearly divisible by 8. So the original number is also divisible by 8.

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

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.

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.

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.

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.