QUICK DIVISIBILITY TRICKS

Divisibility by 2: 

If last digit of the number is even i.e. 0,2,4,6,8
Ex : 876999578 is divisible by 2.

Divisibility by 3: 

If the sum of digits is divisible by 3.
Ex: 327 is divisible by 3, since sum of its digits = (3+2+7) = 12, which is divisible by 3.

Divisibility by 4: 

If the last two digits of the number is divisible by 4.
Ex: 2648 is divisible by 4, since the number formed by the last two digits is 48 which is divisible by 4.

Divisibility by 5: 

If the last digit of the number ends with 0 or 5.
Ex: 20870 ends in a 0, so it is divisible by 5.

 

Divisibility by 6: If the number is divisible by both 2 & 3.
Ex: 558 is divisible by 6, because it is divisible by 2(number is even) as well as 3 (5+5+8=18,which is divisible by 3).

 

 

Divisibility by 7: 

·      Take the last digit of the number you’re testing and double it.

·      Subtract this number from the rest of the digits in the original number.

·      If this new number is either 0 or if it’s a number that’s divisible by 7, then you know that the original number is also divisible by 7. If you can’t easily tell yet if the new number is divisible by 7, go back to the first step with this new smaller number and try again.

For example, is the number 203 divisible by 7? Well, let’s use our three step process to find out:

·      The last digit of 203 is 3, so double that is 3 x 2 = 6.

·      Subtracting this new number, 6, from 20 (the remaining digits of the original number 203) gives 14.

·      Since 14 is divisible by 7, we can immediately tell that the original number, 203, must also be divisible by 7.

Let’s try a larger number. Is 2,023 divisible by 7?

·      The last digit of 2,023 is 3, so double that is 6.

·      Subtracting 6 from 202 (the remaining digits from 2,023) gives us 202 – 6 = 196.

·      Is 196 divisible by 7? I’m not sure. So, let’s repeat the process using the new number 196. The final digit of 196 is 6, so twice that is 12. Subtracting this from 19 (the remaining digits of 196) leaves us with 19 – 12 = 7. Since 7 certainly is divisible by 7, we immediately know that the original number, 2,023, is divisible by 7 too!

 

Divisibility by 8: 

If the last three digits of the number are divisible by 8.
Ex: 3652736 is divisible by 8 because last three digits (736) is divisible by 8.
Note: Rule of divisibility by 2 & 4 on the last three-digit number will not be applicable here. You have to check the divisibility manually.
Ex: 516 is divisible by 2 & 4 but not by 8.

 

 

Divisibility by 9: 

If the sum of the digits is divisible by 9.
Ex: 672381 is divisible by 9, since sum of digits = (6+7+2+3+8+1) = 27 is divisible by 9.

 

Divisibility by 10: 

If the digit at units place is 0 it is divisible by 10.
Ex: 697420, 243540 is divisible by 10.

 

Divisibility by 11: 

If the difference of ‘sum of its digits at odd places’ and ‘sum of its digits at even places’ is either 0 or a number divisible by 11.

Ex: 4832718 is divisible by 11, since:
(Sum of digits at odd places) and (sum of digits at even places)
= (8+7+3+4)-(1+2+8) = 11

 

Divisibility by 12: 

A number is divisible by 12 if it is divisible by both 4 and 3.
Ex: 34632
(i) The number formed by last two digits is 32, which is divisible by 4
(ii) Sum of digits = (3+4+6+2) = 18, which is divisible by 3.

 

Divisibility by 14:

If a number is divisible by both 2 & 7.

Divisibility by 15: 

If a number is divisible by both 3 & 5.