Memorize these rules!
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:
| 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 |
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