Divisibility Rule For 9 With Examples
Divisibility Rule For 9 With Examples
Divisibility Rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
Steps to Check Divisibility by 9
- Add the Digits: Calculate the sum of all the digits in the number.
- Check the Sum: Determine if the resulting sum is divisible by 9.
Example
Example 1: 729
- Add the Digits:
- ( 7 + 2 + 9 = 18)
- Check the Sum:
- ( 18/9 = 2) (with no remainder).
- Conclusion: Since 18 is divisible by 9, 729 is also divisible by 9.
Example 2: 234
- Add the Digits:
- ( 2 + 3 + 4 = 9)
- Check the Sum:
- ( 9/9 = 1) (with no remainder).
- Conclusion: Since 9 is divisible by 9, 234 is also divisible by 9.
Example 3: 56
- Add the Digits:
- ( 5 + 6 = 11)
- Check the Sum:
- ( 11/9 = 1.22) (not an integer, remainder exists).
- Conclusion: Since 11 is not divisible by 9, 56 is not divisible by 9.
Example 4: 999
- Add the Digits:
- ( 9 + 9 + 9 = 27)
- Check the Sum:
- ( 27/9 = 3) (with no remainder).
- Conclusion: Since 27 is divisible by 9, 999 is also divisible by 9.
Example 5: 1,234
- Add the Digits:
- ( 1 + 2 + 3 + 4 = 10)
- Check the Sum:
- ( 10/9 = 1.11) (not an integer, remainder exists).
- Conclusion: Since 10 is not divisible by 9, 1,234 is not divisible by 9.
Summary
To determine if a number is divisible by 9:
- Calculate the sum of its digits.
- Check if that sum is divisible by 9.
If the sum is divisible by 9, then the original number is also divisible by 9.