Tests for Divisibility

Divisibility by 2

If we observe a few multiples of 2 to be 2,4,6,8,10,12,14,...
that is the unit place of these numbers are like 0 , 2 , 4 , 6 , 8.
hence we can conclude that a number is divisible by 2 if that number has any of the digits
 0 , 2 , 4 , 6 ,or  8 in its units place.

Divisibility by 3

If the sum of the digits is a multiple of 3, then the number is divisible by 3.
Example
669 , here first we have to add all the digits
6+6+9 = 21
21 is divisible by 3
hence 669 is divisible by 3

Divisibility by 4

A number with 3 or more digits is divisible by 4 if the last two digits of the given number is divisible by 4.
Example
8216
lets consider the last two digits
16 which is divisible by 4
hence 8216 is divisible by 4

Divisibility by 5

A number which has either 0 or 5 in its units place then that number is divisible by 5.

Divisibility by 6

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

Divisibility by 8

If the number formed by the last three digits is divisible by 8 then that number is divisible by 8.

Example
86512
lets consider the last three digits 512 which is divisible by 8.
hence 86512 is divisible by 8

Divisibility by 9

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

Example
504
lets add all the digits
5+0+4 = 9 which is divisible by 9
hence 504 is divisible by 9

Divisibility by 10

If the number has 0 in its units place then that number is divisible by 10

Divisibility by 11

First we have to find the difference between the sum of the digits at odd places (from the right side)
and the sum of the digits at even places of the number.If the difference is either 0 or that number is divisible by 11 then the given number is divisible by 11.
Example
61809
9+8+6 = 23
0+1=1
their difference = 23-1 = 22 which is divisible by 11
hence 61809 is divisible by 11