The divisibility rule for 7 is a helpful guideline to determine if a given number is divisible by 7 without performing long division.

Here’s how the divisibility rule for 7 works:

- Take the number you want to check for divisibility by 7.
- Double the last digit of the number (the units digit) and subtract it from the remaining truncated number (without the units digit).
- If the resulting number is divisible by 7 (including zero), then the original number is also divisible by 7. Otherwise, it is not divisible by 7.

**Let’s illustrate this rule with an example:**

Example: Determine if the number 686 is divisible by 7.

- The last digit of the number is 6. Double this digit: 6 x 2 = 12.
- Subtract the doubled digit from the truncated number: 68 – 12 = 56.
- The resulting number, 56, is divisible by 7. Therefore, the original number 686 is also divisible by 7.

**Let’s try another example:**

Example: Determine if the number 435 is divisible by 7.

- The last digit of the number is 5. Double this digit: 5 x 2 = 10.
- Subtract the doubled digit from the truncated number: 43 – 10 = 33.
- The resulting number, 33, is not divisible by 7. Therefore, the original number 435 is not divisible by 7.

By applying this divisibility rule, you can quickly determine if a given number is divisible by 7. It is a helpful technique to simplify divisibility checks and perform quick mental calculations.

Divisibility Check

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