Divisibility Rule of 6 with Examples
Last Updated :
22 Oct, 2024
Divisibility rules enable us to easily determine if a number can be divided evenly by another without performing long division.
According to the divisibility rule of 6, a number is divisible by 6 if it is divisible by both 2 and 3.
For Example:
To Check if 138 is divisible by 6.
Check divisibility by 2: The last digit is 8, which is even, so 138 is divisible by 2
Check divisibility by 3: The sum of the digits: 1 + 3 + 8 = 12 which is divisible by 3, so 138 is divisible by 3
Since 138 is divisible by both 2 and 3, 138 is divisible by 6.
More Examples of Divisibility by 6
72 : 72 is divisible by 2 (72 is even) and also divisible by 3 (7 + 2 = 9). So 72 is divisible by 6.
2514 : 2514 is divisible by 2(4 is even) and also divisible by 3 (2 + 5 + 1 + 4 = 12). So 2514 is divisible by 6.
Verification with Table of 6
The following are the numbers in table of 6, even or odd and digit sums:
6 : Even, 6
12 : Even, 1 + 2
18 : Even, 1 + 8
24 : Even, 2 + 4
30 : Even, 3 + 0
36 : Even, 3 + 6
42 : Even, 4 + 2
48 : Even, 4 + 8
54 : Even, 5 + 4
60 : Even, 6 + 0
Other Divisibility Rules:
Solved Examples on Divisibility Rule of 6
Example 1: Check if 342 is divisible by 6
Solution:
- Check divisibility by 2: The last digit is 2, which is even, so 342 is divisible by 2.
- Check divisibility by 3: The sum of the digits is 3 + 4 + 2 = 9.
Since 9 is divisible by 3, 342 is also divisible by 3. Since 342 is divisible by both 2 and 3, it is divisible by 6.
Example 2: Check if 2458 is divisible by 6.
Solution:
- Check divisibility by 2: The last digit is 8, which is even, so 2458 is divisible by 2.
- Check divisibility by 3: The sum of the digits is 2 + 4 + 5 + 8 = 19.
- Since 19 is not divisible by 3, 2458 is not divisible by 3.
Since 2458 is not divisible by 3, it is not divisible by 6.
Example 3: Check if 748392 is divisible by 6
Solution:
- Check divisibility by 2: The last digit is 2, which is even, so 748392 is divisible by 2.
- Check divisibility by 3: The sum of the digits is 7 + 4 + 8 + 3 + 9 + 2 = 33.
Since 33 is divisible by 3 (33 ÷ 3 = 11), 748392 is also divisible by 3.
Since 748392 is divisible by both 2 and 3, it is divisible by 6.
Example 4: Check if 152637485 is divisible by 6.
Solution:
Check divisibility by 2: The last digit is 5, which is not even, so 152637485 is not divisible by 2.
Since 152637485 is not divisible by 2, it is not divisible by 6, even without checking divisibility by 3.
Divisibility Rule of 6 Worksheet
1. Is 4236 divisible by 6?
2. Is 6458 divisible by 6?
3. Is 56760 divisible by 6?
4. Is 89107 divisible by 6?
5. Determine whether 672 is divisible by 6.
6. Check if the number 7890 is divisible by 6.
7. Is the number 435 divisible by 6?
8. Is the number 1542 divisible by 6?
Also Check: Practice Questions on Divisibility Rules