Divisibility Rule For 17 With Examples

Divisibility Rule for 17

The divisibility rule for 17 can be a bit more complex than for smaller numbers, but it can be applied using a specific method. Here’s how it works:

Steps to Check Divisibility by 17

1. Take the Last Digit: Identify the last digit of the number.
2. Multiply the Last Digit by 5: Multiply this last digit by 5.
3. Subtract from the Rest of the Number: Subtract the result from the remaining part of the number (the number without the last digit).
4. Check the Result: If the result is 0 or a multiple of 17, then the original number is divisible by 17. If not, we can repeat the process with the new number.

Example Walkthroughs

Example 1: 221

1. Last Digit: 1
2. Multiply the Last Digit by 5: (1 x 5 = 5)
3. Subtract from the Rest of the Number:

• Remaining number: 22
• Calculation: (22 – 5 = 17)

1. Check the Result:

• 17 is a multiple of 17.
• Conclusion: 221 is divisible by 17.

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Example 2: 289

1. Last Digit: 9
2. Multiply the Last Digit by 5: (9 x 5 = 45)
3. Subtract from the Rest of the Number:

• Remaining number: 28
• Calculation: (28 – 45 = -17)

1. Check the Result:

• (-17) is a multiple of 17.
• Conclusion: 289 is divisible by 17.

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Example 3: 150

1. Last Digit: 0
2. Multiply the Last Digit by 5: (0 x 5 = 0)
3. Subtract from the Rest of the Number:

• Remaining number: 15
• Calculation: (15 – 0 = 15)

1. Check the Result:

• 15 is not a multiple of 17.
• Conclusion: 150 is not divisible by 17.

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Example 4: 102

1. Last Digit: 2
2. Multiply the Last Digit by 5: (2 x 5 = 10)
3. Subtract from the Rest of the Number:

• Remaining number: 10
• Calculation: (10 – 10 = 0)

1. Check the Result:

• 0 is a multiple of 17.
• Conclusion: 102 is divisible by 17.

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Example 5: 51

1. Last Digit: 1
2. Multiply the Last Digit by 5: (1 x 5 = 5)
3. Subtract from the Rest of the Number:

• Remaining number: 5
• Calculation: (5 – 5 = 0)

1. Check the Result:

• 0 is a multiple of 17.
• Conclusion: 51 is divisible by 17.

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Summary

To determine if a number is divisible by 17:

• Identify the last digit and multiply it by 5.
• Subtract this from the remaining part of the number.
• If the result is 0 or a multiple of 17, the original number is divisible by 17.

This method allows we to check divisibility by 17 without performing long division.