Question

what is divisibility rule of 13,17,19​

Answer 1

Divisibility rule of 13

• Multiply the unit digit of the given number by 4
• Then add the result with the remaining digits
• You can resume the same process if you find it difficult to check

For example:

let us take a number "1703". Multiply the unit digit " 3" by 4, we get 12.

Add the result with the remaining digits => (170 + 12) = 182

Now, 182 is divisible by 13.

If you find it difficult to check then resume the same process

Multiply the unit digit of 182 by 4, we get => 2 × 4 = 8

Add the result with the remaining digits => (18 + 8) = 26

Clearly, 26 is divisible by 13.

Divisibility rule of 17

• Multiply the unit digit of the given number by 12
• Then add the result with the remaining digits
• You can resume the same process if you find it difficult to check

For example:

let us take a number "1530". Multiply the unit digit " 0" by 12, we get 0.

Add the result with the remaining digits => (153 + 0) = 153

Now, 153 is divisible by 13.

If you find it difficult to check then resume the same process

Multiply the unit digit of 153 by 12, we get => 3 × 12 = 36

Add the result with the remaining digits => (15 + 36) = 51

Clearly, 51 is divisible by 17.

Divisibility rule of 19

• Multiply the unit digit of the given number by 2
• Then add the result with the remaining digits
• You can resume the same process if you find it difficult to check

For example:

let us take a number "589". Multiply the unit digit " 9" by 2, we get 18.

Add the result with the remaining digits => (58 + 18) = 76

Now, 76 is divisible by 19.

If you find it difficult to check then resume the same process

Multiply the unit digit of 76 by 2, we get => 6 × 2 = 12

Add the result with the remaining digits => (7 + 12) = 19

Clearly, 19 is divisible by 19.

Answer 2

Answer:

The divisibility rule of 13 - Subtract 9 times the last digit from the rest. The result must be divisible by 13.

17- A number is divisible by 17 if you multiply the last digit by 5 and subtract that from the rest. If that result is divisible by 17, then your number is divisible by 17

19- Add two times the last digit to the remaining leading truncated number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary