Divisibility Rule For 14 With Examples
Divisibility Rule For 14 With Examples
Divisibility Rule for 14
A number is divisible by 14 if it meets the criteria for both 2 and 7. This means we need to check two conditions:
- Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- Divisibility by 7: A number is divisible by 7 if, when we apply the specific rule for 7, the result is either 0 or a multiple of 7.
Steps to Check Divisibility by 14
- Check Divisibility by 2:
- Look at the last digit of the number.
- If it is even, proceed to the next step; if it’s odd, the number is not divisible by 14.
- Check Divisibility by 7:
- Use the method for checking divisibility by 7 (either by using the rule for 7 or performing long division).
- Conclusion:
- If both conditions are satisfied, then the number is divisible by 14.
Example Walkthroughs
Example 1: 84
- Check Divisibility by 2:
- Last digit: 4 (even).
- Conclusion: 84 passes this condition.
- Check Divisibility by 7:
- (84/7 = 12) (with no remainder).
- Conclusion: 84 is divisible by 7.
- Final Conclusion: Since 84 is divisible by both 2 and 7, 84 is divisible by 14.
Example 2: 56
- Check Divisibility by 2:
- Last digit: 6 (even).
- Conclusion: 56 passes this condition.
- Check Divisibility by 7:
- (56/7 = 8) (with no remainder).
- Conclusion: 56 is divisible by 7.
- Final Conclusion: Since 56 is divisible by both 2 and 7, 56 is divisible by 14.
Example 3: 30
- Check Divisibility by 2:
- Last digit: 0 (even).
- Conclusion: 30 passes this condition.
- Check Divisibility by 7:
- (30/7 ≈ 4.29) (not an integer, remainder exists).
- Conclusion: 30 is not divisible by 7.
- Final Conclusion: Since 30 is not divisible by 7, it is not divisible by 14.
Example 4: 70
- Check Divisibility by 2:
- Last digit: 0 (even).
- Conclusion: 70 passes this condition.
- Check Divisibility by 7:
- (70/7 = 10) (with no remainder).
- Conclusion: 70 is divisible by 7.
- Final Conclusion: Since 70 is divisible by both 2 and 7, 70 is divisible by 14.
Example 5: 100
- Check Divisibility by 2:
- Last digit: 0 (even).
- Conclusion: 100 passes this condition.
- Check Divisibility by 7:
- (100 /7 ≈ 14.29) (not an integer, remainder exists).
- Conclusion: 100 is not divisible by 7.
- Final Conclusion: Since 100 is not divisible by 7, it is not divisible by 14.
Summary
To determine if a number is divisible by 14:
- First, check if it is even (divisible by 2).
- Then, check if it is divisible by 7.
- If both conditions are met, the number is divisible by 14.
This method allows to quickly verify divisibility without lengthy calculations.