The divisibility rules for 2 are simple. If the last digit of the number is even it is divisible by 2.
So if the number ends in a 0, 2,4,6,8 it is divisible by 2.


Number 
Divisible 
Why? 
66 
yes 
Ends in 6 which is an even number 
203 
No 
3 is not divisible by 2 
48 
yes 
Ends in 8 which is divisible by 2 
In order for a number to be divisible by 6 the number must be an even number and,
If you add the digits together this number must be divisible by 3 

Number 
Divisible by 6? 
Why 
72 
Yes 
72 is an even number and 7+2=9 is divisible by 3 
357 
No 
The number is not even. 
138 
Yes 
The number is even and 1+3+8 =12 is divisible by 3 
In order for a number to be divisible by 8 look at the last three digits and if this number is divisible by 8 then the entire number is divisible by 8 

Number 
Divisible by 8? 
Why 
3648 
Yes 
648/8 = 81 so the number formed by the last three digits is divisible by 8 
5679 
No 
679 is not divisible by 8 so the entire number is not divisible by 8 
In order for a number to be divisible by 9 simply add the digits together and if this number is divisible by 3 and 9 then the entire number is divisible by 9 

Number 
Divisible by 9? 
Why 
234 
Yes 
2+3+4 = 9 which is divisible by 3 and 9 
897 
No 
8+9+7 = 24 which is not divisible 9 
561 
Yes 
5+6+1 = 12 which is divisible by 3 and 9 
In order to be divisible by 10 the number must end in 0 

Number 
Divisible by 10 
Why 
220 
Yes 
Ends in 0 
678 
No 
Does not end in 0 
43780 
Yes 
Ends in 0 
In order for a number to be divisible by 12 it must divisible by 3 and 4 

Number 
Divisible by 12? 
Why 
1044 
Yes 
Is the number divisible by 3 ? 1+4+4=9 which is divisible by 3 and the last two digits 44 is divisible by 4 
204 
Yes 
4+2 =6 which is divisible by 3 and the last two digits 04 is divisible by 4 
878 
No 
The sum of the numbers 8+7+8 = 23 is not divisible by 3 
If the last digit ends in 0 or 5 then it is
divisible by 5 

Number 
Divisible by 5 ? 
Why 
55 
Yes 
55/5 =11 Ends in 5 
456 
No 
456/5 = 91.2 Ends in 6 
650 
yes 
650/5 = 130 Ends in 0 
You have two choices 1. If you combine the last two digits together is their sum divisible by 4? If so, the entire number is divisible by 4 2. Divide the number by 2, and if the sum is even then the number is divisible by four. 

Number 
Divisible by 4 ? 
Why 
56 
Yes 
56/2 = 28 and it is even

786 
No 
786/2 = 393 which is odd or 86 is not divisible by 4 
128 
yes 
128/2 = 64 which is even
or 28 is divisible by 4

The divisibility rules for 3 require one to add the numbers together and see if the product is divisible by three 

Number 
Divisible by 3 ? 
Why 
39 
yes 
9+3 = 12 which is divisible by 3 and passes the divisibility rules 
162 
yes 
1+ 6+2 = 9 which is divisible by 3 
67 
no 
6 + 7 = 15 which is not divisible by 3 therefore does not follow the divisibility rules 