Divisibility Rule For 26 With Examples
Divisibility Rule For 26 With Examples
Divisibility Rule For 26
The divisibility rule for 26 can be derived from its prime factors, specifically (2) and (13). A number is divisible by 26 if it meets the conditions for both of these factors.
To determine if a number is divisible by 26, we can use a straightforward approach. Since 26 is the product of the prime numbers 2 and 13, a number is divisible by 26 if and only if it is divisible by both 2 and 13.
Divisibility Rules
- Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- Divisibility by 13:
- Take the Last Digit: Identify the last digit of the number.
- Multiply that last Last Digit By 4: Multiply the last digit by 4.
- Add from the Rest of the Number: Add this value from the rest of the number.
- Check the Result: If the result is 0 or a multiple of 13, then the original number is divisible by 13. If not, repeat the process with the new number.
Detailed Steps with Examples
Example 1: Check if 156 is divisible by 26
- Check Divisibility by 2:
- Last digit is 6 (even).
- Result: Divisible by 2.
- Check Divisibility by 13:
- Last digit is 6.
- Multiply by 4: (6 x 4 = 24).
- The rest is 15. Add:
[15 + 24 = 39] - Check if 39 is divisible by 13: (39/13 = 3).
- Result: Divisible by 13.
Since 156 is divisible by both 2 and 13, it is divisible by 26.
Example 2: Check if 130 is divisible by 26
- Check Divisibility by 2:
- Last digit is 0 (even).
- Result: Divisible by 2.
- Check Divisibility by 13:
- Last digit is 0.
- Multiply by 4: (0 x 4 = 0).
- The rest is 13. Add:
[13 + 0 = 13] - Check if 13 is divisible by 13: (13/13 = 1).
- Result: Divisible by 13.
Since 130 is divisible by both 2 and 13, it is divisible by 26.
Example 3: Check if 234 is divisible by 26
- Check Divisibility by 2:
- Last digit is 4 (even).
- Result: Divisible by 2.
- Check Divisibility by 13:
- Last digit is 4.
- Multiply by 4: (4 x 4 = 16).
- The rest is 23. Add:
[23 + 16 = 39] - Check if 39 is divisible by 13: (39/13 = 3).
- Result: Divisible by 13.
Since 234 is divisible by both 2 and 13, it is divisible by 26.
Example 4: Check if 78 is divisible by 26
- Check Divisibility by 2:
- Last digit is 8 (even).
- Result: Divisible by 2.
- Check Divisibility by 13:
- Last digit is 8.
- Multiply by 4: (8 x 4 = 32).
- The rest is 7. Add:
[7 + 32 = 39] - Check if 39 is divisible by 13: (39/13 = 3).
- Result: Divisible by 13.
Since 78 is divisible by both 2 and 13, it is divisible by 26.
Example 5: Check if 45 is divisible by 26
- Check Divisibility by 2:
- Last digit is 5 (odd).
- Result: Not divisible by 2.
Since 45 is not divisible by 2, it cannot be divisible by 26. Thus, 45 is not divisible by 26.
Example 6: Check if 104 is divisible by 26
- Check for 2:
- Last digit: 4 (even)
- Conclusion: 104 is divisible by 2.
- Check for 13:
- Last digit: 4
- Add (4 x 4) from the rest of the number (10):
- (10 + 16 = 26)
- Check (26/13 = 2) (no remainder).
- Conclusion: 104 is divisible by 13.
Since 104 is divisible by both 2 and 13, it is divisible by 26.
Example 7: Check if 182 is divisible by 26
- Check for 2:
- Last digit: 2 (even)
- Conclusion: 182 is divisible by 2.
- Check for 13:
- Last digit: 2
- Add (4 x 2) from the rest of the number (18):
- (18 + 8 = 26)
- Check (26/13 = 2) (no remainder).
- Conclusion: 182 is divisible by 13.
Since 182 is divisible by both 2 and 13, it is divisible by 26.
Example 8: Check if 92 is divisible by 26
- Check for 2:
- Last digit: 2 (even)
- Conclusion: 92 is divisible by 2.
- Check for 13:
- Last digit: 2
- Add (4 x 2) from the rest of the number (9):
- (9 + 8 = 17)
- Check (17/13) (not divisible).
- Conclusion: 92 is not divisible by 13.
Since 92 is not divisible by 13, it is not divisible by 26.
Example 9: Check if 364 is divisible by 26
- Check for 2:
- Last digit: 4 (even)
- Conclusion: 364 is divisible by 2.
- Check for 13:
- Last digit: 4
- Add (4 x 4) from the rest of the number (36):
- (36 + 16 = 52)
- Check (52/13 = 4) (no remainder).
- Conclusion: 364 is divisible by 13.
Since 364 is divisible by both 2 and 13, it is divisible by 26.
Example 10: Check if 75 is divisible by 26
- Check for 2:
- Last digit: 5 (odd)
- Conclusion: 75 is not divisible by 2.
Since 75 is not divisible by 2, it is not divisible by 26.
Checking Divisibility by 13
To check divisibility by 13, we can use one of these methods:
- Add 4 times the last digit from the rest of the number and check if the result is divisible by 13.
Combined Rule
To determine if a number is divisible by 26:
- Check if the number is even (divisible by 2).
- Check if the number (or the result from the calculation) is divisible by 13.
Summary
To determine if a number is divisible by 26:
- First, check if it is even (divisible by 2).
- Then, check for divisibility by 13 using the subtraction method.
If both conditions are met, the number is divisible by 26. This method helps in making quick assessments regarding divisibility.