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Divisibility Rules
Posted 06-28-2009 at 03:15 PM by shabbir
One of my friend in an interview faced a question related to prime number and so I thought this would help lot of people to do some of the prime number maths quickly.
Divisibility By 2
All the even numbers are divisible by 2. E.g. Numbers ending in 0,2,4,6,8
Divisibility by 3
Add all the digits of the number and see if its divisible by 3. If the sum is divisible by 3, so is the number
Divisibility by 4
If last two digits in your number are divisible by 4? then the number is too!
Divisibility by 5
Numbers ending in a 5 or a 0 are always divisible by 5.
Divisibility by 6
If the Number is divisible by 2 and 3 it is divisible by 6 also.
Divisibility by 7
Double the last digit and subtract it from the rest. Repeat the process for larger numbers. Example: 637 = 63-7*2 = 49 which is divisible by 7 and so 637.
Divisibility by 8
If the last 3 digits are divisible by 8, so is the entire number.
Divisibility by 9
Add up all the digits in the number. If the sum is divisible by 9, so is the number.
Divisibility by 10
If the number ends in a 0, it is divisible by 10.
Divisibility by 11
Subtract the last digit from the remaining number. If the result is divisible by 11, then the first number would also be.
E.g. 6875 ==> 687-5 = 682,
682 ==> 68-2 = 66 which is divisible by 11 and so 6875
Divisibility By 13
Add four times the last digit to the remaining number. If the result is divisible by 13, then the first number would also be.
Eg. 8281 ==> 828 + 4 = 832
832 ==> 83 + 8 = 91 which is divisible by 13
Divisibility By 17
Subtract five times the last digit from the remaining number. If the result is divisible by 17, then the first number would also be.
Eg 2023 ==> 202 - 15 = 187 is divisible by 17. You should know the table of 17.
Divisibility By 19
Add two times the last digit to the remaining number. If the result is divisible by 19, then first number would also be.
Eg. 75449 ==> 7544 + 18 = 7562
7562 ==> 756 + 4 = 760
760 ==> 76 + 0 = 76 which is divisible by 19
Divisibility By 2
All the even numbers are divisible by 2. E.g. Numbers ending in 0,2,4,6,8
Divisibility by 3
Add all the digits of the number and see if its divisible by 3. If the sum is divisible by 3, so is the number
Divisibility by 4
If last two digits in your number are divisible by 4? then the number is too!
Divisibility by 5
Numbers ending in a 5 or a 0 are always divisible by 5.
Divisibility by 6
If the Number is divisible by 2 and 3 it is divisible by 6 also.
Divisibility by 7
Double the last digit and subtract it from the rest. Repeat the process for larger numbers. Example: 637 = 63-7*2 = 49 which is divisible by 7 and so 637.
Divisibility by 8
If the last 3 digits are divisible by 8, so is the entire number.
Divisibility by 9
Add up all the digits in the number. If the sum is divisible by 9, so is the number.
Divisibility by 10
If the number ends in a 0, it is divisible by 10.
Divisibility by 11
Subtract the last digit from the remaining number. If the result is divisible by 11, then the first number would also be.
E.g. 6875 ==> 687-5 = 682,
682 ==> 68-2 = 66 which is divisible by 11 and so 6875
Divisibility By 13
Add four times the last digit to the remaining number. If the result is divisible by 13, then the first number would also be.
Eg. 8281 ==> 828 + 4 = 832
832 ==> 83 + 8 = 91 which is divisible by 13
Divisibility By 17
Subtract five times the last digit from the remaining number. If the result is divisible by 17, then the first number would also be.
Eg 2023 ==> 202 - 15 = 187 is divisible by 17. You should know the table of 17.
Divisibility By 19
Add two times the last digit to the remaining number. If the result is divisible by 19, then first number would also be.
Eg. 75449 ==> 7544 + 18 = 7562
7562 ==> 756 + 4 = 760
760 ==> 76 + 0 = 76 which is divisible by 19
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