Divisibility Rule For 7 With Examples

Divisibility Rule for 7

Determining if a number is divisible by 7 can be a bit trickier than other rules, but it can be done using a straightforward method:

Rule

To check if a number is divisible by 7:

1. Take the last digit of the number.
2. Double that last digit.
3. Subtract the doubled value from the rest of the number (the part of the number that remains when we remove the last digit).
4. If the result is either 0 or a multiple of 7, then the original number is divisible by 7.

Step-by-Step Process

1. Identify the last digit of the number.
2. Double the last digit.
3. Subtract the doubled value from the remaining number.
4. Check the result:

• If the result is 0 or divisible by 7, the original number is divisible by 7.

Examples

Example 1: 203

1. Last digit: 3
2. Double it: (3 x 2 = 6)
3. Subtract from remaining number: (20 – 6 = 14)
4. Check the result: 14 is divisible by 7.

• Conclusion: 203 is divisible by 7.

Example 2: 154

1. Last digit: 4
2. Double it: (4 x 2 = 8)
3. Subtract from remaining number: (15 – 8 = 7)
4. Check the result: 7 is divisible by 7.

• Conclusion: 154 is divisible by 7.

Example 3: 65

1. Last digit: 5
2. Double it: (5 x 2 = 10)
3. Subtract from remaining number: (6 – 10 = -4)
4. Check the result: -4 is not divisible by 7.

• Conclusion: 65 is not divisible by 7.

Example 4: 777

1. Last digit: 7
2. Double it: (7 x 2 = 14)
3. Subtract from remaining number: (77 – 14 = 63)
4. Check the result: 63 is divisible by 7 (since (63 ÷ 7 = 9)).

• Conclusion: 777 is divisible by 7.

Example 5: 1001

1. Last digit: 1
2. Double it: (1 x 2 = 2)
3. Subtract from remaining number: (100 – 2 = 98)
4. Check the result: 98 is divisible by 7 (since (98 ÷ 7 = 14)).

• Conclusion: 1001 is divisible by 7.

Summary

To determine if a number is divisible by 7:

• Take the last digit, double it, subtract it from the rest of the number, and check if the result is divisible by 7.