Divisibility Rule of 19: Rule, Examples

Divisibility Rule of 19

A number is divisible by 19 if doubling the last digit and adding it to the rest of the number results in a multiple of 19 (like 0, 19, 38, 57, etc.).

If the new number is still large, repeat the steps until you get a smaller number that is easy to check!

Steps to Check Divisibility by 19

1. Take the last digit of the number.

2. Double it (Multiply it by 2).

3. Add this number to the remaining part of the number.

4. If the result is a multiple of 19, then the original number is divisible by 19! 🎉

5. If the result is still large, repeat the process until you get a small number.

Examples

Example 1: Is 133 divisible by 19?

1. Take the last digit: 3

2. Double it: 3 × 2 = 6

3. Add it to the remaining number: 13 + 6 = 19

4. 19 is a multiple of 19 (19 ÷ 19 = 1)

133 is divisible by 19.

Example 2: Is 437 divisible by 19?

1. Take the last digit: 7

2. Double it: 7 × 2 = 14

3. Add it to the remaining number: 43 + 14 = 57

4. 57 is a multiple of 19 (57 ÷ 19 = 3)

437 is divisible by 19.

Example 3: Is 528 divisible by 19?

1. Take the last digit: 8

2. Double it: 8 × 2 = 16

3. Add it to the remaining number: 52 + 16 = 68

4. 68 is not a multiple of 19.

528 is not divisible by 19.

Try It Yourself:

Are they divisible by 19?
1. 266
2. 988
3. 1520