Divisibility Rule For 29 With Examples

Divisibility Rule For 29

The divisibility rule for 29 is not as straightforward as for smaller numbers, but it can still be applied using a systematic approach.

To determine if a number is divisible by 29, we can use a specific rule: take three times the last digit of the number and add it to the rest of the digits. If the result is divisible by 29, then the original number is also divisible by 29.

Here’s a detailed explanation of how to check for divisibility by 29.

To determine if a number is divisible by 29, we can use the following method:

1. Direct Division: The simplest way is to divide the number by 29 and check if the result is an integer (i.e., there is no remainder).
2. Alternative Method: For larger numbers, we can use the following process:

• Remove the last digit of the number.
• Multiply that digit by 3.
• Add the result from the remaining number.
• If the result is divisible by 29, then the original number is also divisible by 29.

Step-by-Step Process

1. Identify the Last Digit: Take the last digit of the number.
2. Multiply the Last Digit by 3: Multiply this last digit by 3.
3. Remove the Last Digit: Take the rest of the number (the part without the last digit).
4. Add: Add the result from step 2 to the result from step 3.
5. Check for Divisibility: If the resulting number is divisible by 29, then the original number is also divisible by 29.

Examples

Example 1: Check if 145 is divisible by 29

1. Direct Division:

• (145/29 = 5) (exactly, with no remainder).
• Conclusion: 145 is divisible by 29.

Example 2: Check if 1234 is divisible by 29

1. Direct Division:

• (1234/29 ≈ 42.55) (not an integer).
• Conclusion: 1234 is not divisible by 29.

Example 3: Check if 348 is divisible by 29

1. Using the Alternative Method:

• Last digit: 8, remaining number: 34
• Multiply the last digit by 3: (8 x 3 = 24)
• Add from the remaining number: (34 + 24 = 58)
• (58/29) (not divisible).
• Conclusion: 348 is not divisible by 29.

Example 4: Check if 870 is divisible by 29

1. Using the Alternative Method:

• Last digit: 0, remaining number: 87
• Multiply the last digit by 3: (0 x 3 = 0)
• Add from the remaining number: (87 + 0 = 87)
• (87/29 = 3) (exactly, with no remainder).
• Conclusion: 870 is divisible by 29.

Example 5: Check if 1015 is divisible by 29

1. Using the Alternative Method:

• Last digit: 5, remaining number: 101
• Multiply the last digit by 3: (5 x 3 = 15)
• Add from the remaining number: (101 + 15 =116)
• (116/29 = 4) (exactly, with no remainder)
• Conclusion: 1015 is divisible by 29.

Example 6: Check if 1014 is divisible by 29

1. Using the Alternative Method:

• Last digit: 4, remaining number: 101
• Multiply the last digit by 3: (4 x 3 = 12)
• Add from the remaining number: (101 + 12 = 113)
• (113/29 ≈ 3.89) (not an integer).
• Conclusion: 1014 is not divisible by 29.

Example 7: Check if 1740 is divisible by 29

1. Using the Alternative Method:

• Last digit: 0, remaining number: 174
• Multiply the last digit by 3: (0 x 3 = 0)
• Add from the remaining number: (174 + 0 = 174)
• (174/29 = 6) (exactly, with no remainder).
• Conclusion: 1740 is divisible by 29.

Example 8: Check if 116 is divisible by 29

1. Last Digit: 6
2. Multiply by 3: (3 x 6 = 18)
3. Rest of the Number: 11
4. Add: (11 + 18 = 29)
5. Check Divisibility: 29 is divisible by 29.

Conclusion: 116 is divisible by 29.

Example 9: Check if 145 is divisible by 29

1. Last Digit: 5
2. Multiply by 3: (3 x 5 = 15)
3. Rest of the Number: 14
4. Add: (14 + 15 = 29)
5. Check Divisibility: 29 is divisible by 29.

Conclusion: 145 is divisible by 29.

Example 10: Check if 235 is divisible by 29

1. Last Digit: 5
2. Multiply by 3: (3 x 5 = 15)
3. Rest of the Number: 23
4. Add: (23 + 15 = 38)
5. Check Divisibility: 38 is not divisible by 29.

Conclusion: 235 is not divisible by 29.

Example 11: Check if 289 is divisible by 29

1. Last Digit: 9
2. Multiply by 3: (3 x 9 = 27)
3. Rest of the Number: 28
4. Add: (28 + 27 = 55)
5. Check Divisibility: 55 is not divisible by 29.

Conclusion: 289 is not divisible by 29.

Summary

To determine if a number is divisible by 29:

1. Directly divide the number by 29 and check for a remainder.
2. Alternatively, use the method of removing the last digit, multiplying it by 3, and adding from the remaining number to check for divisibility.

Using this method allows we to quickly assess the divisibility of a number by 29 without long division.

This method helps in making quick assessments, especially for larger numbers.