Divisibility Rules
Easily test if one number can be evenly divided by another
Divisible By
"Divisible By" means "If you divide one number by another, is the result a whole number?"
Example, 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 can be evenly divided by another, without having to do too much calculation!
A number is
divisible by: |
If: |
Example: |
| 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)
7019 is not
|
| 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:
(Note: you can apply this rule to that answer again if you want) |
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=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
221 is not
|
| 11 |
If you sum every second digit and then subtract all other digits and the answer is:
|
1364 ((3+4) - (1+6) = 0) Yes
3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
|
| 12 |
The number is divisible by both 3 and 4 |
648 (6+4+8=18 and 18÷3=6, also 48÷4=12) Yes
916 (9+1+6=16, 16÷3= 5 1/3) No
|
There are lots more! Not only are there divisibility tests for larger numbers, but there are more tests for the numbers we have shown.
|
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