Divisibility Rule For 31 With Examples
Divisibility Rule For 31 With Examples
Divisibility Rule for 31
The divisibility rule for 31 is less straightforward than for smaller numbers, but it can be applied using a systematic approach. Here’s a detailed explanation of how to check if a number is divisible by 31, along with examples.
The divisibility rule for 31 states that a number is divisible by 31 if, after applying a specific operation involving its digits, the result is divisible by 31. The rule involves multiplying the last digit of the number by 3, subtracting this result from the rest of the number and then checking if the final result is divisible by 31.
To determine if a number is divisible by 31, we can use the following method:
- Direct Division: The simplest way is to divide the number by 31 and check if the result is an integer (i.e., there is no remainder).
- Alternative Method: For larger numbers, we can use the following process:
- Remove the last digit of the number.
- Multiply that digit by 3.
- Subtract the result from the remaining number.
- If the result is divisible by 31 (including if it’s 0), then the original number is also divisible by 31.
Steps of the Rule:
- Identify the Number: Choose a number we want to check for divisibility by 31.
- Separate the Digits: Identify the last digit and the rest of the number.
- Multiply the Last Digit by 3: Take the last digit and multiply it by 3.
- Subtract from the Rest: Subtract the result from the number formed by the remaining digits.
- Check the Result: Determine if the final result is divisible by 31. If it is, then the original number is also divisible by 31.
Example 1: Check if 124 is divisible by 31
- Identify the Number: 124
- Separate the Digits: Last digit = 4, Rest of the number = 12
- Multiply the Last Digit by 3: (4 x 3 = 12)
- Subtract from the Rest: (12 – 12 = 0)
- Check the Result: 0 is divisible by 31. Therefore, 124 is divisible by 31.
Example 2: Check if 195 is divisible by 31
- Identify the Number: 195
- Separate the Digits: Last digit = 5, Rest of the number = 19
- Multiply the Last Digit by 3: (5 x 3 = 15)
- Subtract from the Rest: (19 – 15 = 4)
- Check the Result: 4 is not divisible by 31. Therefore, 195 is not divisible by 31.
Example 3: Check if 372 is divisible by 31
- Identify the Number: 372
- Separate the Digits: Last digit = 2, Rest of the number = 37
- Multiply the Last Digit by 3: (2 x 3 = 6)
- Subtract from the Rest: (37 – 6 = 31)
- Check the Result: 31 is divisible by 31. Therefore, 372 is divisible by 31.
Example 4: Check if 625 is divisible by 31
- Identify the Number: 625
- Separate the Digits: Last digit = 5, Rest of the number = 62
- Multiply the Last Digit by 3: (5 x 3 = 15)
- Subtract from the Rest: (62 – 15 = 47)
- Check the Result: 47 is not divisible by 31. Therefore, 625 is not divisible by 31.
Examples
Example 1: Check if 124 is divisible by 31
- Direct Division:
- (124/31 = 4) (exactly, with no remainder).
- Conclusion: 124 is divisible by 31.
Example 2: Check if 130 is divisible by 31
- Direct Division:
- (130/31≈ 4.19) (not an integer).
- Conclusion: 130 is not divisible by 31.
Example 3: Check if 961 is divisible by 31
- Using the Alternative Method:
- Last digit: 1, remaining number: 96
- Multiply the last digit by 3: (1 x 3 = 3)
- Subtract from the remaining number: (96 – 3 = 93)
- (93/31 = 3) (exactly, with no remainder).
- Conclusion: 961 is divisible by 31.
Example 4: Check if 505 is divisible by 31
- Using the Alternative Method:
- Last digit: 5, remaining number: 50
- Multiply the last digit by 3: (5 x 3 = 15)
- Subtract from the remaining number: (50 – 15 = 35)
- (35/31 ≈1.13) (not an integer).
- Conclusion: 505 is not divisible by 31.
Example 5: Check if 1000 is divisible by 31
- Direct Division:
- (1000/31≈ 32.26) (not an integer).
- Conclusion: 1000 is not divisible by 31.
Example 6: Check if 1551 is divisible by 31
- Using the Alternative Method:
- Last digit: 1, remaining number: 155
- Multiply the last digit by 3: (1 x 3 = 3)
- Subtract from the remaining number: (155 – 3 = 152)
- (152/31≈ 4.9) (not an integer).
- Conclusion: 1551 is not divisible by 31.
Example 7: Check if 1862 is divisible by 31
- Using the Alternative Method:
- Last digit: 2, remaining number: 186
- Multiply the last digit by 3: (2 x 3 = 6)
- Subtract from the remaining number: (186 – 6 = 180)
- (180/31≈ 5.8) (not an integer).
- Conclusion: 1862 is not divisible by 31.
Summary of the Rule
- The rule provides a quick way to check divisibility by 31 without performing full division.
- If the result after subtraction is still a large number, we can repeat the process to simplify it further.
- This method is useful for both mental math and manual calculations.
To determine if a number is divisible by 31:
- Directly divide the number by 31 and check for a remainder.
- Alternatively, use the method of removing the last digit, multiplying it by 3, and subtracting from the remaining number to check for divisibility.
Practicing this rule with different numbers can help we become more proficient at determining divisibility by 31.
This method helps in making quick assessments, especially for larger numbers.