Divisibility Rules (Tests)

Divisible By:

If

Examples

2

The number is even. Or The last(units) digit of the number is 0, 2, 4, 6 or 8

84 is divisible by 2.
85 is not divisible by 2.

3

The sum of the digits of number is divisible by 3.

1248 is divisible by 3.
(1 + 2 + 4 + 8 = 15)

346 is not divisible by 3.
(3 + 4 + 6 = 13)

4

The last two digits of the number is divisible by 4. And the numbers having two or more zeros at the end.

23456 is divisible by 4.
(56 is divisible by 4)

13000 is divisible by 4.
(Two or more zeros at the end.)

5

The numbers having 0 or 5 at the end.

12345 is divisible by 5.
(5 is there at the end)

1234 is not divisible by 5.
(0 or 5 is not there at the end)

6

The number is divisible by both 2 and 3.

5358 is divisible by 6.
(It is divisible by both 2 and 3)

6782 is not divisible by 6.
(It is divisible by 2 but not divisible by 3)

7

The difference between twice the units digit and the number formed by other digits is either 0 or divisible by 7.

861 is divisible by 7.
[86 – (1 × 2)) = 84 which is divisible by 7]

21 is divisible by 7.
[2 – (1 × 2)) = 0]

868 is divisible by 7.
[86 – (8 × 2)) = 70 which is divisible by 7]

8

The number formed by last three digits is divisible by 8. And the numbers having three or more zeros at the end.

2056 is divisible by 8.
(056 is divisible by 8)

13000 is divisible by 8.
(Three zeros at last)

9

The sum of all the digits is divisible by 9.

5301 is divisible by 9.
(5 + 3 + 0 + 1 = 9 which is divisible by 9)

10

The number ends with zero.

467590 is divisible by 10.
(It ends with zero)

11

The difference between the sum of digits at even places and sum of digits at odd places is 0 or divisible by 11.

10538 is divisible by 11.
[(1 + 5 + 8) – (0 + 3) =  11 which is divisible by 11]

724867 is divisible by 11.
[(7 + 4 + 6) – (2 + 8 + 7) = 0]

12

The number is divisible by both 3 and 4.

5472 is divisible by 12.
( The number is divisible by both 3 and 4)

5475 is not divisible by 12.
(The number is divisible by 3 but not divisible by 4)

13

Method: Multiply last digit of the number by 4 and add it to the remaining number. Continue this process until two digit number is achieved. If this two digit number is divisible by 13 then the number is divisible by 13.

182 is divisible by 13.
(Multiply last digit by 4 i.e 2×4 = 8.
Add it to the remaining number i.e 18 + 8 = 26.
26 is divisible by 13 so 182 is divisible by 13)

2145 is divisible by 13
( Multiply last digit by 4 i.e 5×4 = 20.
Add it to the remaining number i.e 214 + 20 = 234 which is not a two digit number so repeat the process.
Multiply last digit of 234 by 4 i.e. 4×4= 16.
Add it to the remaining number i.e 23 + 16 = 39 which is divisible by 13 so 2145 is divisible by 13)

14

The number is divisible by both 2 and 7.

7966 is divisible by 14.
(The number is divisible by both 2 and 7)

15

The number is divisible by both 3 and 5.

3525 is divisible by 15.
(The number is divisible by both 3 and 5)

16

The number formed by last four digits is divisible by 16.

41104 is divisible by 16.
(The number formed by last four digits is divisible by 16)

17

Method: Multiply last digit with 5 and subtract it from the remaining number. If the result is divisible by 17 then the original number is also divisible by 17. Repeat this process if required.

4029 is divisible by 17
( Multiply last digit by 5 i.e. 9×5= 45.
Subtract it from the remaining number.
402 – 45 = 357 which is divisible by 17 so 4029 is divisible by 17)

18

The number is even and divisible by 9.

4428 is divisible by 18.
(It is even and divisible by 9)

19

Method: Multiply last digit with 2 and add it to the remaining number. If the result is divisible by 19 then original number is also divisible by 19. Repeat this process if required.

1235 is divisible by 19.
(Multiply last digit with 2 i.e 5×2 = 10.
Add it to the remaining number 123 i.e 123 + 10 = 133 which is divisible by 19 so 1235 is also divisible by 19)