Divisibility Rules of 5, 10, 7 and 11
Concept: The Divisibility Rules help us to determine if a number will divide into another number without actually having to divide. Rules can be made for any of the number but here we will learn the most common ones. Here we talk about Divisibility Rules of Mathematics for numbers 3, 6, and 9
Prerequisite: Person should know basic tables.
1. Divisibility Rule for 5:
If the number ends with ‘5’ or ‘0’
Example: 505 here last digit is 5 so number is divisible by 5
|
Number |
Divisible? | Why? |
|
10910 |
Yes |
Last Digit is 0 so number is divisible by 5 |
| 918 | No |
Last Digit is 8 so not divisible by 5 |
2. Divisibility Rule for 10:
If the number ends with ‘0’
Example: 500 here last digit is 0 which is divisible by 10
|
Number |
Divisible? | Why? |
|
1910 |
Yes |
Last Digit is 0 so number is divisible by 10 |
| 188 | No |
Last Digit is 8 so not divisible by 10 |
3. Divisibility Rule for 7:
Double the last digit and subtract it from a number made by the rest of the truncated digits.
Example: 672 here last digit is 2 (Double of this is 4) so final number will be (67 – 4) = 63 which is divisible by 7
|
Number |
Divisible? | Why? |
|
4704 |
Yes |
Last Digit is 4 (Double = 8) so final number is (470 – 8) = 462 divisible by 7 |
| 5145 | Yes |
Last Digit is 5 (Double = 10) so final number is (514 – 10) = 504 divisible by 7 |
4. Divisibility Rule for 11:
Add and subtract digits in an alternating pattern (add first, subtract second, add third)
Example: 1364 so pattern will (1-3+6-4) = 0 which is divisible by 11
|
Number |
Divisible? | Why? |
| 9273 | Yes |
Pattern will be (9-2+7-3) = 11 which is divisible by 11 |