Divisibility Rules
Easily test if one number can be evenly divided by another
Divisible By
"Divisible By" means "when you divide one number by another the result is a whole number"
Examples:
14 is divisible by 7, because 14÷7 = 2 exactly
But 15 is not divisible by 7, because 15÷7 = 2 ^{1}/_{7} (i.e., the result is not a whole number)
The Divisibility Rules
These rules let you test if one number is divisible by another, without having to do too much calculation!
Divisible by:  If:  Examples: 

2  The last digit is even (0,2,4,6,8)  128 is 129 is not 
3  The sum of the digits is divisible by 3 
381 (3+8+1=12, and 12÷3 = 4) Yes 217 (2+1+7=10, and 10÷3 = 3 ^{1}/_{3}) No 
4  The last 2 digits are divisible by 4 
1312 is (12÷4=3) 
5  The last digit is 0 or 5  175 is 809 is not 
6  The number is divisible by both 2 and 3 
114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes 308 (it is even, but 3+0+8=11 and 11÷3 = 3 ^{2}/_{3}) No 
7  If you double the last digit and subtract it from the rest of the number and
the answer is:

672 (Double 2 is 4, 674=63, and 63÷7=9) Yes 905 (Double 5 is 10, 9010=80, and 80÷7=11 ^{3}/_{7}) No 
8  The last three digits are divisible by 8 
109816 (816÷8=102) Yes 216302 (302÷8=37 ^{3}/_{4}) No 
9  The sum of the digits is divisible by 9 (Note: you can apply this rule to that answer again if you want) 
1629 (1+6+2+9=18, and again, 1+8=9) Yes 2013 (2+0+1+3=6) No 
10  The number ends in 0 
220 is 
11  Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc). Then the answer must be:

1364 (1−3+6−4 = 0) Yes 913 (9−1+3 = 11) Yes 3729 (3−7+2−9 = −11) Yes 987 (9−8+7 = 8) No 
12  The number is divisible by both 3 and 4 
648 524 
There are lots more! Not only are there divisibility tests for larger numbers, but there are more tests for the numbers we have shown.
Factors Can Be Useful
Factors are the numbers you multiply to get another number:
This can be useful, because:
When a number is divisible by another number ...
... then it is also divisible by each of the factors of that number.
Example: If a number is divisible by 6, it is also divisible by 2 and 3
Example: If a number is divisible by 12, it is also divisible by 2, 3, 4 and 6
Another Rule For 11
 Subtract the first digit from a number made by the other digits.
 If that number is divisible by 11 then the original number is, too.
Can repeat this if needed,
Example: 286
28 − 6 is 22, which is divisible by 11, so 286 is divisible by 11
Example: 14641
 1464 − 1 is 1463
 146 − 3 is 143
 14 − 3 is 11, which is divisible by 11, so 14641 is divisible by 11