Divisibility rules for 2,3,4,5,6,7,8,9,10,11,13,15,17,19.

Hello everyone,

Today I’m going to explain the concept of

  Divisibility

Division

    •    Divisibility:– This is the best way to predict whether any number is divisible by any other whole number or not without doing calculation.

interesting…!!!? isn’t it ?
yes, of course…!!!
by following the rules we can identify this.
now I’m going to explain each rule,

  • Test of Divisibility of 2 :-

If any number ends with an even number

example  290, 156, 654 etc.

  • Test of Divisibility of 3 :-

If the sum of digits of any number is divisible by 3 then the number is divisible by 3.
example 54/3
 = 5+4 = 9   
 9/3= 3
hence 54 is also divisible by 3 
i.e. 54/3 = 18
but if it is 53 
then 5+3 =8 which is not divisible by 3 so 53 will also not divisible by 3.

  • Test of Divisibility of 4 :

A number is divisible by 4 if the number formed by last two digits is divisible by 4 
example  316 /4 = 79
here 16 is forming by last two digits which is divisible by 4.

  • Test of Divisibility of 5 :- 

A number is divisible by 5 if the last digit of that number is either 5 or 0.
example  545
545/5 = 109
620/5 = 124

  • Test of Divisibility of 6 :-

A number which is divisible by 2 and 3 both, means the number should satisfy the Divisibility of 2 and 3, then the number must be divisible by 6.
example  168 
168/2 = 84
168/3 = 56
now 
168/6 = 28.

  • Test of Divisibility of 8 :-

A number is divisible by 8 if the number is formed by it’s last three digit is divisible by 8.
example . 7,120
so 120 last three digit number is divisible by 8 120/8 = 15
hence 7,120 will also be divisible by 8
7,120/8= 890

  • Test of Divisibility of 9 :-

it is likely to the rule for number 3
A number is divisible by 9 if the sum of the number is divisible by 9.
example . 549 
5+4+9 =18
18/9= 2
hence 
549 /9 = 61

  • Test of Divisibility of 10 :

Any number which ends with 0 will be divisible by 10.
example 10, 100, 1000, 10000…

  • Test of Divisibility of 7 :-

Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary.
Example: 826. Twice 6 is 12. So take 12 from the truncated 82. Now 82-12=70. This is divisible by 7, so 826 is divisible by 7 also.

There are similar rules for the remaining primes under 50, i.e. 11,13, 17,19,23,29,31,37,41,43 and 47.






  • Test for divisibility by 11:- 

Subtract the last digit from the remaining leading truncated number. If the result is divisible by 11, then so was the first number. Apply this rule over and over again as necessary.
Example: 19151–> 1915-1 =1914 –>191-4=187 –>18-7=11, so yes, 19151 is divisible by 11.

  • Test for divisibility by 13.

Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.
Example: 50661–>5066+4=5070–>507+0=507–>50+28=78 and 78 is 6*13, so 50661 is divisible by 13.

  • Test for divisibility by 17.

Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.
Example: 3978–>397-5*8=357–>35-5*7=0. So 3978 is divisible by 17.

  • Test for divisibility by 19.

Add two times the last digit to the remaining leading truncated number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.

example : 101156–>10115+2*6=10127–>1012+2*7=1026–>102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

So I tried to collect the best explanation of Divisibility.
If you are any doubts and if you have suggestions then comment under this article.
Thank you,

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