DIVISIBILITY RULES

Divisibility Math Tricks to Learn the Facts (Divisibility)


Dividing by 2
  1. All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.
Dividing by 3
  1. Add up all the digits in the number.
  2. Find out what the sum is. If the sum is divisible by 3, so is the number
  3. For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

Dividing by 4
  1. Are the last two digits in your number divisible by 4?
  2. If so, the number is too!
  3. For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.
Dividing by 5
  1. Numbers ending in a 5 or a 0 are always divisible by 5.
Dividing by 6
  1. If the Number is divisible by 2 and 3 it is divisible by 6 also.
Dividing by 7 (2 Tests)
  • Take the last digit in a number.
  • Double and subtract the last digit in your number from the rest of the digits.
  • Repeat the process for larger numbers.
  • Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

    NEXT TEST
  • Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary
  • Add the products.
  • If the sum is divisible by 7 - so is your number.
  • Example: Is 2016 divisible by 7?
  • 6(1) + 1(3) + 0(2) + 2(6) = 21
  • 21 is divisible by 7 and we can now say that 2016 is also divisible by 7.
Dividing by 8
  1. This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.
  2. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.
Dividing by 9
  1. Almost the same rule and dividing by 3. Add up all the digits in the number.
  2. Find out what the sum is. If the sum is divisible by 9, so is the number.
  3. For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!
Dividing by 10
  1. If the number ends in a 0, it is divisible by 10.                           

Dividing by 11

The sum of the even digits is subtracted from the sum of the odd digits. The result is either 0 or divisible by 11.

Example : 
i) 292215
ii) 760672 

Explanation : 
i) 292215 
By rule, (9+2+5) - (2+2+1) = 11 

ii) 760672 
By rule, (6+6+2) - (7+0+7) = 0 

Both the numbers can be divided by 11.


Divisbility Rule of 12 :

Number divisible by both 3 and 4.

Example : 
i) 9012 
ii) 23988

Explanation : 
i) 9012
a) rule of divisible by 3,
sum of the digits, 9 + 0 + 1 + 2 = 12/3 = 4 
b) rule of divisible by 4,
last two digits = 12/4 = 3 

ii) 23988
a) rule of divisible by 3,
sum of the digits, 2 + 3 + 9 + 8 + 8 = 30/3 = 10 
b) rule of divisible by 4,
last two digits = 88/4 = 22

Both the numbers can be divided by 12
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