In this article, we will learn about divisibility rule of 17 with example. i.e. We will see how to check if any number is divisible by 17 or not.

What is Divisibility Rule of 17 ?

To check if number is divisible by 17, follow below steps –

1. Take the last digit of the number, multiply it by 5, and subtract it from the rest of the number without the last digit.
2. If the result is divisible by 17, then the original number is also divisible by 17. If the result is not divisible by 17, then the original number is not divisible by 17.

Example 1

Is 655420 divisible by 17?
Solution:

Follow below steps to check it –

1. The last digit is 0. So, we will skip last and check for number without last digit if new number is divisible by 17 or not. In this case, we take the previous digit from new number 65542, which is 2. multiply it by 5 to get 10, and subtract it from the rest of the number without the last digit: 65542 – 10 = 65532.
2. To check if 65532 is divisible by 17, we can use long division or mental arithmetic. Since 65532 is not an obvious multiple of 17, we can use long division to check. By doing so, we get that 65532 is not divisible by 17. So, 655420 is not divisible by 17.

Example 2

Check if 176 is divisible by 17 or not.
Solution:

Follow steps below to check it –

1. The units digit of 176 is 6.
2. The remaining digits are 17.
3. Multiply the units digit by 5 = 6 x 5= 30.
4. The difference between result and the remaining digits is 30 – 17 = 13.

Since 13 is not divisible by 17, 176 is NOT divisible by 17.

Example 3

Is  235 divisible by 17 ?
Solution:

Follow steps below to check it –

1. The units digit of 235 is 5.
2. The remaining digits are 23.
3. Multiply the units digit by 5 = 5 x 5 = 25.
4. The difference between result and the remaining digits is 25 – 23 = 2.

Since 2 is NOT divisible by 17, 235 is NOT divisible by 17.

Example 4

Is 2572 divisible by 17?
Solution:

To check if 2572 is divisible by 17 or not, we need to find if the difference between five times the unit digit and the remaining digits is divisible by 17.

In given number, 2572, the unit digit is 2. So, we need to check if the difference between 5 times 2 (i.e., 10) and the remaining digits (i.e., 257) is divisible by 17.

10 – 257 = -247

Since -247 is not divisible by 17, so 2572 is NOT divisible by 17.