An integer is divisible by 7 if, after applying a specific algorithm, the result is 0 or a multiple of 7.
The Divisibility Rule for 7
To determine if an integer is divisible by 7, follow these steps:
- Remove the last digit: Take the integer and separate the last digit from the remaining digits.
- Double the last digit: Multiply the removed digit by 2.
- Subtract from the remaining digits: Subtract the doubled digit from the remaining digits.
- Check the result: If the result is 0 or divisible by 7, the original number is divisible by 7. Otherwise, it's not.
Example: Let's check if 91 is divisible by 7.
- Remove the last digit: 9 | 1
- Double the last digit: 1 * 2 = 2
- Subtract from the remaining digits: 9 - 2 = 7
- Check the result: 7 is divisible by 7. Therefore, 91 is divisible by 7.
Another Example: Let's check 343.
- Remove the last digit: 34 | 3
- Double the last digit: 3 * 2 = 6
- Subtract from the remaining digits: 34 - 6 = 28
- Check the result: 28 is divisible by 7 (28 / 7 = 4). Therefore, 343 is divisible by 7.
Why this works: This method is based on modular arithmetic. The process repeatedly reduces the number until it becomes small enough to easily check for divisibility by 7. While not immediately obvious, this algorithm consistently produces a number congruent to the original number modulo 7.
Multiple sources confirm this method: Smartick, Testbook, Byju's, and others reiterate this algorithm for determining divisibility by 7.
