Divisibility Rule of 19

The divisibility rule for 19 states that a number is divisible by 19 if the following condition is met:

Divisibility by 19: To determine if a number is divisible by 19,

Step 1:Double the last digit.
Step 2: Add this doubled value to the remaining parts of the number.
Step 3: Check if the result is divisible by19.

If the resulting sum is divisible by 19, the original number is also divisible.

Alternate Rule for Divisibility by 19

Group the digits of the number in sets of three from right to left. Then, alternately sum and subtract these groups. If the result is divisible by 19, the original number is divisible by 19.

Examples on Divisibility Rule of 19

Example 1: Check divisibility of 1234567 by 19.

Solution:

Group as 1, 234, 567.
Then alternately sum and subtract: 567 − 234 + 1 = 334

Since 334 is not divisible by 19, 1234567 is not divisible by 19.

Example 2: Check divisibility of 29303814 by 19.

Solution:

Group as 29,303,814.
Then alternately sum and subtract: 814 − 303 + 29 = 540

Since 540 is divisible by 19, 29,303,814 is also divisible by 19.

Example 3:Check if 102 is divisible by 19.

Solution:

1. Double the last digit: 2 × 2 = 4.

2. Add to remaining digits: 10 + 4 = 14.

3. Check divisibility: 12 ÷ 19 = 0.6315 (not divisible).

Since, 12 is not divisible by 19, 102 is also not divisible by 19.

Example 4:Check if 2675 is divisible by 19.

Solution:

1. Double the last digit: 5 × 2 = 10

2. Add to remaining digits: 267 + 10 = 277

3. Check divisibility: 277 ÷ 19 = 14.579 (not divisible).

Since, 277 is not divisible by 19, 2675 is not divisible by 19.

Example 5: Check if 3610 is divisible by 19.

Solution:

1. Double the last digit: 0 × 2 = 0

2. Add to remaining digits: 361 + 0 = 361

3. Check divisibility: 361 ÷ 19 = 19(divisible).

Since, 361 is divisible by 19, 3610 is also divisible by 19.

Read other Divisibility Rules:

• Divisibility Rules from 1 to 19
• Divisibility Rule for 3
• Divisibility Rule for 7
• Divisibility Rule of 9
• Divisibility Rules of 11
• Divisibility Rules of 13

Worksheet: Divisibility Rule of 19

You can download free worksheet on Divisibility Rule of 19 from below:

Also Check: Practice Questions on Divisibility Rules.