# Divisibility Rules

This topic would deal with divisibility rules. There are certain divisibility rules of certain numbers which help in determining that by which number the given number is divisible. Divisibility rules are an effective tool for determining with which numbers a given number is divisible.

Here is a list of divisibility rule of certain number:

Divisibility Rule of 2:

Numbers ending with 0, 2 4, 6, or 8 are divisible by 2

For Example: 64 is divisible by 2 as the number ends with 4

Divisibility Rule of 3:

If the sum of the digits of a given number is divisible by 3 then the whole number I divisible by 3

For Example: 345 is divisible by 3 as 3 + 4 + 5 = 12. 12 is divisible by 3 hence the number 345 is divisible by 3

Divisibility Rule of 4:

If the last two digits of the number I divisible by 4 then the whole number is divisible by 4

For Example: 45784 is divisible by 4 as the last two digits 84 is divisible by 4. 84 divided by 4 is 21. Hence the number 45784 is divisible by 4

Divisibility Rule of 5:

If a number ends with 0 or 5 then the number is divisible by 5.

For Example: 50 is divisible by 5 as 50 ends with the number 0

Divisibility Rule of 6:

If a number is divisible by both 2 and 3 then the number is divisible by 6

For Example: 36 is divisible by both 2 and 3 hence 36 is divisible by 6 as well

Divisibility Rule of 7:

If after subtracting the twice the last digit from the remaining digit of the number gives a number that is multiple of 7 then the whole number is a multiple of 7.

For Example: 343 is divisible by 7. The last digit is 3 so 34 – 3 × 2 = 28. Now 28 is divisible by 7 hence the number 343 is also divisible by 7

Divisibility Rule of 8:

If the last three digits are divisible by 8 then the number is also divisible by 8.

For Example: 80648 is divisible by 8 as 648 is divisible by 8 and the quotient is 81. Hence, 80648 is also divisible by 8

Divisibility Rule of 9:

If the sum of the digits is divisible by 9 then the given number is also divisible by 9

For Example: 8910 = 8 + 9 + 1 + 0 = 27. Now since 27 is divisible by 9 the number 8910 is divisible by 9

Divisibility rule of 10

If the last digit of the number is 0 then the number is divisible by 10

For Example: 840 is divisible by 10 as the last digit is 0

Divisibility Rule of 11:

If the difference of the sum of the digits at odd and even places is divisible by 11 or is zero then the number is divisible by 11.

For Example: 1331

Sum of the digits at odd places = 1 + 3 = 4

Sum of the digits at even places = 3 + 1 = 4

The difference = 4 – 4 = 0. Hence, 1331 is divisible by 11

Divisibility Rule of 12:

if a number is divisible by both 3 and 4 then the number is divisible by 12

For Example: 144 is divisible by 3 and 4 hence divisible by 12 as well