Divisibility Rules of 3, 6 and 9
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 3:
If the sum of the digits is a multiple of 3 or divisible by 3, then complete number is said to be divisible by 3.
Example: 31941
Step 1: Add up the digits given above. 3 + 1 + 9 + 4 + 1 = 18
Step 2: To determine if 3 divides sum of 18. Yes.
Step 3: So number 31941 is divisible by 3.
| Number | Divisible? | Why? |
| 903 | Yes | 3903 = (3+9+0+3) => 15 which is a multiple of 3 |
| 918 | Yes | 114918 = (1+1+4+9+1+8) => 18 which is a multiple of 3 |
| 2017 | No | 2017 = (2+0+1+7) = 10 which is not a multiple of 3 |
2. Divisibility Rule for 9
If the sum of the digits is a multiple of 9 or divisible by 9, then complete number is said to be divisible by 9.
Example: 9405
Step 1: Add up the digits given above 9 + 4 + 0 + 5 = 18
Step 2: To determine if 9 divides sum of 18. Yes.
Step 3: So number 9405 is divisible by 9.
| Number | Divisible? | Why? |
| 98910 | Yes | 98010 = (9+8+0+1+0) => 18 which is a multiple of 9 |
| 190188 | Yes | 190188 = (1+9+0+1+8+8) => 27 which is a not multiple of 9 |
| 21188 | No | 21188 = (2+1+1+8+8) => 20 which is a not multiple of 9 |
3. Divisibility Rule for 6
If the sum of the digits is a divisible by both 2 and 3 as we know 6 is formed by multiplication of 2 and 3 (2 * 3)
Example: 504
So in 504 the last digit is ‘4’ which is multiple of 2 so divisible by 2
and 504 = (5+0+4) => 9 which is multiple of 3 so divisible by 3,
Hence complete number is divisible by 6
|
Number |
Divisible? |
Why? |
|
5106 |
Yes | Last Digit is 6 so divisible by 2 and 5106 = (5+1+0+6) => 12 which is a multiple of 3 |
| 2017 | No |
Last Digit is 7 which is not divisible by 2, so need no check for multiple of 3. So answer is NO |