Divisibility Rules and Test
Divisibility test of 2:
If the last digit of any number is an even number i.e. 0, 2, 4, 6, 8 then the number will be divisible by 2.
Example: 478798
Here last digit is 8 (even number), therefore 478798 is divisible by 2.
Divisibility test of 3:
If sum of the digits of the given number is divisible by 3, then the given number will be divisible by 3.
Example: 59875902
Here sum of the digits = 5 + 9 + 8 + 7 + 5 + 9 + 0 + 2 = 45
Since 45 is divisible by 3 ( 45 = 15 x 3), therefore 59875902 is divisible by 3.
Divisibility test of 4:
If last two digits of the given number is divisible by 4, then the given number will be divisible by 4.
Example: 987439716
Here last two digits is 16, which is divisible by 4 (16 = 4 x 4), therefore 987439716 is divisible by 4.
Divisibility test of 5:
If the last digit of any number is 0 or 5, then the number will be divisible by 5.
Example: 4830825 or 80697580
Here in both the numbers last digit is 5 and in the 2nd last digit is 0.
Therefore, 4830825 or 80697580 are divisible by 5.
Divisibility test of 6:
If the last digit of any number is divisible by 2 and 3 both, then the whole number will be divisible by 6.
Example: 854994
Here last digit is 4 which is divisible by 2, therefore the whole number is divisible by 2 and sum of all digits i.e. 8 + 5 + 4 + 9 + 9 + 4 = 39, again 3+ 9 = 12, which is divisible by 3 , therefore the whole number is divisible by 3.
Since the number is divisible by 2 and 3 both therefore 854994 is divisible by 6.
Divisibility test of 7:
For checking Divisibility test of 7 we take an example to make it clear.
Taking the number 343
Double the last digit , last digit = 3, After doubling it 3 x 2 = 6
Subtract it from the rest digit i.e. 34 ─ 6 = 28 which is divisible by 7, therefore whole number is divisible by 7. If after doing this step still you get a big number and unable to find that is it divisible by 7 or not? You can repeat this step.
Divisibility test of 8:
If last three digits of the given number is divisible by 8, then the given number will be divisible by 8.
Example: 987439816
Here last three digits is 816, which is divisible by 8 (816 = 102 x 8), therefore 987439716 is divisible by 8.
Divisibility test of 9:
If sum of the digits of the given number is divisible by 9, then the given number will be divisible by 9.
Example: 59875902
Here sum of the digits = 5 + 9 + 8 + 7 + 5 + 9 + 0 + 2 = 45
Since 45 is divisible by 9 ( 45 = 5 x 9), therefore 59875902 is divisible by 9.
Divisibility test of 10:
If the last digit of any number is 0 , then the number will be divisible by 10.
Example: 80697580
Here the number’s last digit is 0.
Therefore, 80697580 are divisible by 10.
Divisibility test of 11:
For checking Divisibility test of 11 we take an example to make it clear.
Taking the number 1331, Placing the digits of the number 1331 in serial wise as 1st , 2nd , 3rd 4th places as shown below.
1st
|
2nd
|
3rd
|
4th
|
1
|
3
|
3
|
1
|
If the sum of odd places digits i.e. 1st and 3rd digits = the sum of even places digits i.e. 2nd and 4th place digits or difference between odd place digits and even place digits should be zero or multiple of 11, then the given number will be divisible by 11.
Here
Sum of odd places digits i.e. 1st and 3rd digits = 1 + 3 = 4
Sum of even places digits i.e. 2nd and 4th digits = 3 + 1 = 4
difference between Sum of odd places digits and Sum of even places digits = 4 ─ 4 = 0
Therefore 1331 is divisible by 11.