Divisibility Rule For 13 With Examples

Divisibility Rule for 13

The divisibility rule for 13 is a bit more complex than those for smaller numbers like 2 or 5, but it can still be useful for quickly determining whether a number is divisible by 13.

Here’s how it works, along with detailed examples.

Steps to Check Divisibility by 13

To check if a number ( n ) is divisible by 13, we can follow these steps:

1. Take the Last Digit: Identify the last digit of the number.
2. Multiply that last Last Digit By 4: Multiply the last digit by 4.
3. Add from the Rest of the Number: Add this value from the rest of the number.
4. Check the Result: If the result is 0 or a multiple of 13, then the original number is divisible by 13. If not, repeat the process with the new number.

Example Walkthroughs

Step-by-Step Example

Let’s go through the rule with a couple of examples.

Example 1: Check if 273 is divisible by 13

1. Last digit: 3
2. Multiply by 4: ( 3 x 4 = 12 )
3. Add from the rest of the number: The rest of the number is 27 (from 273).

• ( 27 + 12 = 39 )

1. Check if the result is divisible by 13:

• 39 is divisible by 13.

Conclusion: 273 is divisible by 13.

Example 2: Check if 455 is divisible by 13

1. Last digit: 5
2. Multiply by 4: ( 5 x 4 = 20 )
3. Subtract from the rest of the number: The rest of the number is 45 (from 455).

• ( 45 +20 = 65 )

1. Check if the result is divisible by 13:

• 65 is divisible by 13.

Conclusion: 455 is divisible by 13.

Example 3: Check if 200 is divisible by 13

1. Last digit: 0
2. Multiply by 4: ( 0 x 4 = 0 )
3. Add from the rest of the number: The rest of the number is 20 (from 200).

• ( 20 + 0 = 20 )

1. Check if the result is divisible by 13:

• ( 20/13 = 1.538 ) (not an integer).

Conclusion: 200 is not divisible by 13.

Further Example with a Larger Number

Example 4: Check if 1049 is divisible by 13

1. Last digit: 9
2. Multiply by 4: ( 9 x 4 = 36 )
3. Add from the rest of the number: The rest of the number is 104 (from 1049).

• ( 104 + 36 = 140 )

1. Check if the result is divisible by 13:

• ( 140/13 = 10.76) (not an integer).

Conclusion: 1049 is not divisible by 13.

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Summary

To determine if a number is divisible by 13:

• Take the last digit of the number.
• Multiply that last digit by 4.
• Add this from the remaining number.
• If the result is 0 or a multiple of 13, the original number is divisible by 13.

The rule works effectively for both small and larger numbers, helping we quickly determine divisibility by 13.

Remember that we can apply this rule repeatedly if needed, especially with larger results.