Divisibility Rule For 12 With Examples
Divisibility Rule For 12 With Examples
Divisibility Rule for 12
A number is divisible by 12 if it is divisible by both 3 and 4. This means we need to check two conditions:
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisibility by 4: A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4.
Steps to Check Divisibility by 12
- Check Divisibility by 3:
- Add the digits of the number.
- Check if the sum is divisible by 3.
- Check Divisibility by 4:
- Look at the last two digits of the number.
- Determine if that two-digit number is divisible by 4.
- Conclusion:
- If both conditions are met, then the original number is divisible by 12.
Example Walkthroughs
Example 1: 144
- Check Divisibility by 3:
- Digits: 1, 4, 4
- Sum: (1 + 4 + 4 = 9)
- (9/3 = 3) (with no remainder).
- Check Divisibility by 4:
- Last two digits: 44
- (44/4 = 11) (with no remainder).
- Conclusion: Since 144 is divisible by both 3 and 4, 144 is divisible by 12.
Example 2: 240
- Check Divisibility by 3:
- Digits: 2, 4, 0
- Sum: (2 + 4 + 0 = 6)
- (6/3 = 2) (with no remainder).
- Check Divisibility by 4:
- Last two digits: 40
- (40/4 = 10) (with no remainder).
- Conclusion: Since 240 is divisible by both 3 and 4, 240 is divisible by 12.
Example 3: 350
- Check Divisibility by 3:
- Digits: 3, 5, 0
- Sum: (3 + 5 + 0 = 8)
- (8/3 ≈2.67) (not an integer, remainder exists).
- Check Divisibility by 4:
- Last two digits: 50
- (50/4 = 12.5) (not an integer, remainder exists).
- Conclusion: Since 350 is not divisible by 3, it is not divisible by 12.
Example 4: 720
- Check Divisibility by 3:
- Digits: 7, 2, 0
- Sum: (7 + 2 + 0 = 9)
- (9/3 = 3) (with no remainder).
- Check Divisibility by 4:
- Last two digits: 20
- (20/4 = 5) (with no remainder).
- Conclusion: Since 720 is divisible by both 3 and 4, 720 is divisible by 12.
Example 5: 85
- Check Divisibility by 3:
- Digits: 8, 5
- Sum: (8 + 5 = 13)
- (13/3 ≈ 4.33) (not an integer, remainder exists).
- Check Divisibility by 4:
- Last two digits: 85
- (85/4 = 21.25) (not an integer, remainder exists).
- Conclusion: Since 85 is not divisible by 3, it is not divisible by 12.
Summary
To determine if a number is divisible by 12:
- Check if the sum of its digits is divisible by 3.
- Check if the last two digits form a number that is divisible by 4.
- If both conditions are satisfied, the number is divisible by 12.
This method efficiently verifies divisibility by 12 without performing long division.