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)
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 |
There are lots more! Not only are there divisibility tests for larger numbers, but there are more tests for the numbers we have shown.
In the Next Post I will tell you how to check divisibility by ANY NUMBER.
The link to Next Post is This.
The link to Next Post is This.
Actually this is the method to generate Divisibility Rules For Any Number.
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