New divisibility rule of 7
A new divisibility rule!
Here's a new divisibility rule for 7:
Rule: A number is divisible by 7 if and only if the difference between the number and the nearest multiple of 7 is also divisible by 7.
Example: Let's test the number 217.
- Find the nearest multiple of 7: 217 is closer to 210 (7 × 30) than 224 (7 × 32), so we'll use 210.
- Calculate the difference: 217 - 210 = 7
- Check if the difference is divisible by 7: 7 is indeed divisible by 7 (since 7 = 7 × 1).
- Since the difference is divisible by 7, the original number 217 is also divisible by 7.
Why it works: This rule is based on the fact that the remainder when dividing a number by 7 is the same as the remainder when dividing the difference between the number and the nearest multiple of 7 by 7. If the difference is divisible by 7, then the original number must also be divisible by 7.
Note: This rule is not as well-known as some other divisibility rules, but it's a useful addition to your toolkit for testing divisibility by 7.