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:

  1. Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
  2. 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

  1. 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.
  1. Check Divisibility by 7:
  • Use the method for checking divisibility by 7 (either by using the rule for 7 or performing long division).
  1. Conclusion:
  • If both conditions are satisfied, then the number is divisible by 14.

Example Walkthroughs

Example 1: 84

  1. Check Divisibility by 2:
  • Last digit: 4 (even).
  • Conclusion: 84 passes this condition.
  1. Check Divisibility by 7:
  • (84/7 = 12) (with no remainder).
  • Conclusion: 84 is divisible by 7.
  1. Final Conclusion: Since 84 is divisible by both 2 and 7, 84 is divisible by 14.

Example 2: 56

  1. Check Divisibility by 2:
  • Last digit: 6 (even).
  • Conclusion: 56 passes this condition.
  1. Check Divisibility by 7:
  • (56/7 = 8) (with no remainder).
  • Conclusion: 56 is divisible by 7.
  1. Final Conclusion: Since 56 is divisible by both 2 and 7, 56 is divisible by 14.

Example 3: 30

  1. Check Divisibility by 2:
  • Last digit: 0 (even).
  • Conclusion: 30 passes this condition.
  1. Check Divisibility by 7:
  • (30/7 ≈ 4.29) (not an integer, remainder exists).
  • Conclusion: 30 is not divisible by 7.
  1. Final Conclusion: Since 30 is not divisible by 7, it is not divisible by 14.

Example 4: 70

  1. Check Divisibility by 2:
  • Last digit: 0 (even).
  • Conclusion: 70 passes this condition.
  1. Check Divisibility by 7:
  • (70/7 = 10) (with no remainder).
  • Conclusion: 70 is divisible by 7.
  1. Final Conclusion: Since 70 is divisible by both 2 and 7, 70 is divisible by 14.

Example 5: 100

  1. Check Divisibility by 2:
  • Last digit: 0 (even).
  • Conclusion: 100 passes this condition.
  1. Check Divisibility by 7:
  • (100 /7 ≈ 14.29) (not an integer, remainder exists).
  • Conclusion: 100 is not divisible by 7.
  1. 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.

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