Divisibility Rules
Divisible By
- "Divisible By" means "when you divide one number by another the result is a whole number"
- "Divisible by" and "can be evenly divided by" mean the same thing
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
| 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)
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
(By 3? 6+4+8=18 and 18÷3=6 Yes. By 4? 48÷4=12 Yes) Yes
524
(By 3? 5+2+4=11, 11÷3= 3 2/3 No. Don't need to check by 4.) No |
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
Exerpt from:
http://www.mathsisfun.com/divisibility-rules.html
