Divisibility Rule For 19 With Examples

Divisibility Rule For 19

The divisibility rule for 19 is not as straightforward as rules for smaller numbers, but it can be approached systematically.

To check if a number is divisible by 19, we can use the following method:

Here’s how to apply it step by step:

Step-by-Step Explanation

1. Identify the number: Take the number we want to check for divisibility by 19.
2. Separate the last digit: Extract the last digit of the number and remember the rest of the number without the last digit.
3. Double the last digit: Multiply the last digit by 2.
4. Addition: Add the doubled last digit from the rest of the number.
5. Check for divisibility: If the result is multiple of 19, then the original number is divisible by 19. If not, it is not divisible.

1. Take the last digit of the number.
2. Multiply that last digit by 2.
3. Add this value to the rest of the number.
4. If the result is divisible by 19, then the original number is also divisible by 19.

Example 1: Checking if 256 is divisible by 19

1. Number: 256
2. Last digit: 6 (the rest is 25)
3. Double the last digit: (2 x 6 = 12)
4. Add: (25 + 12 = 37)
5. Check for divisibility: 37 is not a multiple of 19, so 256 is not divisible by 19.

Example 2: Checking if 361 is divisible by 19

1. Number: 361
2. Last digit: 1 (the rest is 36)
3. Double the last digit: (2 x 1 = 2)
4. Add: (36 + 2 = 38)
5. Check for divisibility: 38 is a multiple of 19, so 361 is divisible by 19.

Example 3: Checking if 437 is divisible by 19

1. Number: 437
2. Last digit: 7 (the rest is 43)
3. Double the last digit: (2 x 7 = 14)
4. Add: (43 + 14 = 57)
5. Check for divisibility: 57 is a multiple of 19, so 437 is divisible by 19.

Example 4: Checking if 399 is divisible by 19

1. Number: 399
2. Last digit: 9 (the rest is 39)
3. Double the last digit: (2 x 9 = 18)
4. Add: (39 + 18 = 57)
5. Check for divisibility: 57 is a multiple of 19, so 399 is divisible by 19.

Example 5: Checking if 760 is divisible by 19

1. Number: 760
2. Last digit: 0 (the rest is 76)
3. Double the last digit: (2 x 0 = 0)
4. Add: (76 + 0 = 76)
5. Check for divisibility: 76 is a multiple of 19, so 760 is divisible by 19.

Examples:

1. Example: 456

• Last digit: 6
• Multiply by 2: (6 x 2 = 12)
• Add to the rest: (45 + 12 = 57)
• Check 57:
  • (57/19 = 3) (which is an integer)
• 456 is divisible by 19.

1. Example: 209

• Last digit: 9
• Multiply by 2: (9 x 2 = 18)
• Add to the rest: (20 + 18 = 38)
• Check 38:
  • (38/19 = 2) (which is an integer)
• 209 is divisible by 19.

1. Example: 399

• Last digit: 9
• Multiply by 2: (9 x 2 = 18)
• Add to the rest: (39 + 18 = 57)
• Check 38:
  • (57/19 = 3) (which is an integer)
• 399 is divisible by 19.

1. Example: 418

• Last digit: 8
• Multiply by 2: (8 x 2 = 16)
• Add to the rest: (41 + 16 = 57)
• Check 57:
  • (57/19 = 3) (which is an integer)
• 418 is divisible by 19.

1. Example: 76

• Last digit: 6
• Multiply by 2: (6 x 2 = 12)
• Add to the rest: (7 + 12 = 19)
• Check 19:
  • (19/19 = 1) (which is an integer)
• 76 is divisible by 19.

While the rule for 19 may not be as intuitive as for smaller numbers, it provides a systematic way to check divisibility. By following the steps of doubling the last digit and adding from the rest of the number, we can determine if a number is divisible by 19.

Conclusion

To determine if a number is divisible by 19, use the process of multiplying the last digit by 2 and adding it to the rest of the number. If the result is divisible by 19, then the original number is also divisible by 19.