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# Divisibility Rule of 7

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:

1. Take the number you want to check for divisibility by 7.
2. Double the last digit of the number (the units digit) and subtract it from the remaining truncated number (without the units digit).
3. 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.

1. The last digit of the number is 6. Double this digit: 6 x 2 = 12.
2. Subtract the doubled digit from the truncated number: 68 – 12 = 56.
3. 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.

1. The last digit of the number is 5. Double this digit: 5 x 2 = 10.
2. Subtract the doubled digit from the truncated number: 43 – 10 = 33.
3. 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

Divisibility Check