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.

Know the divisibility rule of 3 here.

Try It Yourself:

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

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FAQs

 

1. What is the Divisibility Rule of 19?

To check if a number is divisible by 19:

1. Multiply the last digit by 2.

2. Subtract it from the rest of the number.

3. Repeat the steps if needed.

4. If the result is 0 or divisible by 19, then the original number is divisible by 19.

2. How to check divisibility by 19? 

• Take the last digit of the number.

• Double it (×2).

• Subtract it from the rest of the number (without the last digit).

• If the result is 0 or divisible by 19, the whole number is divisible by 19.

• Repeat the steps if the number is still large.

3. Is 361 divisible by 19? 

To check if 361 is divisible by 19, we use the divisibility rule or directly divide the number.

Step 1: Use the divisibility rule
Last digit: 1 → 1 × 2 = 2
36 − 2 = 34 → Not divisible by 19
So, 361 fails the rule.

Step 2: Direct division
361 ÷ 19 = 19 (no remainder) 
So, 361 is divisible by 19.