How can you tell if a number is divisible by 7?

A number is divisible by 7 if, after performing a specific calculation on its digits, the result is either 0 or a multiple of 7.

Divisibility Rule of 7 Explained

The divisibility rule for 7 is a bit more involved than rules for smaller numbers, but it's effective. Here's how it works, as stated in the reference:

• Step 1: Isolate the Last Digit: Take the last digit of the number you want to test.
• Step 2: Double the Last Digit: Multiply the last digit by 2.
• Step 3: Subtract from the Rest of the Number: Take the remaining digits of the original number (everything except the last one) and subtract the result from Step 2.
• Step 4: Check the Difference: If the result from Step 3 is either 0 or a number that is divisible by 7, then the original number is also divisible by 7.

Here's a summary table for easy reference:

Step	Action
1	Isolate the last digit
2	Double the last digit
3	Subtract from remaining number
4	Check if result is 0 or multiple of 7

Examples

Let's see some examples of how to apply this rule:

• Example 1: 357

  1. Last digit: 7
  2. Double the last digit: 7 * 2 = 14
  3. Remaining number: 35
  4. Subtract: 35 - 14 = 21. 21 is divisible by 7 (21/7 = 3), so 357 is divisible by 7.

• Example 2: 548

  1. Last digit: 8
  2. Double the last digit: 8 * 2 = 16
  3. Remaining number: 54
  4. Subtract: 54 - 16 = 38. 38 is not divisible by 7, therefore 548 is not divisible by 7.

• Example 3: 105

  1. Last digit: 5
  2. Double the last digit: 5 * 2 = 10
  3. Remaining number: 10
  4. Subtract: 10 - 10 = 0. 0 is considered divisible by 7 so 105 is divisible by 7.

Practical Insights

• For larger numbers, you can repeatedly apply this rule until you get a smaller number that you can easily recognize as divisible by 7 or not.
• Keep in mind that this rule only tests divisibility by 7.
• If you have a calculator it is often quicker and simpler to just divide the number by 7 and look for a whole number.