Divisibility Rule of 17

The divisibility rule for 17 states that a number is divisible by 17 if the following condition holds:

Divisibility by 17: To check divisibility by 17,

Step 1: Multiply the last digit by 5.
Step 2: Subtract this product from the remaining digits of the number.
Step 3: Check if the result is divisible by 17.

If the result is 0 or a number that can be divided evenly by 17, then the original number is divisible by 17.

Alternate Divisibility Rule of 17

Other then this there are some more rules which can also be used to check divisibility by 17. Some of these are:

Alternate Rule 1

Take the number formed by the last two digits of the given number. Multiply the rest of the number by 2. Subtract this product from the number formed by the last two digits. If the result is 0 or divisible by 17, the original number is divisible by 17.

Example: Check if 442 is divisible by 17.

1. Take the last two digits: 42.
2. Multiply the remaining part (4) by 2: 4 × 2 = 8.
3. Subtract the product from the last two digits: 42 - 8 = 34.
4. Check if 34 is divisible by 17: 34 ÷ 17 = 2 (a whole number).

So, 442 is divisible by 17.

Alternate Rule 2

Find the sum of 9 times the last digit and 5 times the rest of the number. If the sum is 0 or divisible by 17, the original number is divisible by 17.

Example: Check if 289 is divisible by 17.

1. Last digit: 9.
2. Rest of the number: 28.
3. Calculate: 9 × 9 = 81 and 5 × 28 = 140.
4. Sum: 81 + 140 = 221.
5. Check if 221 is divisible by 17: 221 ÷ 17 = 13 (a whole number).

Since the result is divisible by 17, 289 is divisible by 17.

Other Divisibility Rules:

• Divisibility Rule for 3
• Divisibility Rule for 7
• Divisibility Rules of 11
• Divisibility Rules of 13

Divisibility Rule of 17: Worksheet

You can download free worksheet on Divisibility Rule of 17 from below:

Also Check: Practice Questions on Divisibility Rules.