Divisibility of Numbers

a) Divisibility by 2: A number is divisible by 2 if its last digit is 0,2,4,6,8.

b) Divisibility by 3: If the sum of all digits if a given number is divisible by 3 means then the number will be divisible by 3.

Example 1: 108

sol:  1+0+8=9  Here 9 is divisible by 3 so the entire number is divisible by 3.

Example 2: 745=7+4+5=16, Here 16 is not divisibility by 3, so 745 is not divisible by 3.

c) Divisibility by 4: A number is divisible by 4 if and only if its last 2 digits are divisible by 4.

Example: 528 

sol: Its last 2 digits are   28 is divisible by 4, so 528  is divisible by 4.

d) Divisibility by 5:

 If the last digit of a given number is a 0 or 5 then the entire number will be divisible by 5.

Example: 560,495 etc.

e) Divisibility by 6: If the given number is divisible by both 2 and 3 then the number will be divisible by 6

Example: 144

sol: It is divisible by 2

1+4+4=9   so, it is divisible by 3

so 144 is divisible by 6

f) Divisibility by 9: If the sum of all the digits in a given number is divisible by 9 means then the given number will be divisible by 9.

Example: 4608

sol: 4+6+0+8=18  it is divisible by 9

so 4608 is divisible by 9.

g) Divisibility by 10: If the last digit of a given number is '0' then the entire number will be divisible by 10.

Example: 520     

sol: the last digit of a given number is 0  so it is divisible by 10.