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** Yes, there is a rule to check if a number is divisible by 7 without actually dividing it. It is, however, a little different than that of 2,3,5 etc. There are 2 rules. **

*RULE 1:*

- Remove the last digit
- Double the last digit
- Subtract it from the truncated original number (i.e. the original number without the last digit)
- Continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7.

EXAMPLE

Is 12264 divisible by 7 without leaving any remainder?

- Remove the last digit: 1226
- Double the last digit: 4 x 2 = 8
- Subtract it: 1226 - 8 = 1218
- Repeat the above steps
- 121 - 8 x 2
- = 121 - 16
- = 105

- 121 - 8 x 2
- Repeat the above steps
- 10 - 5 x 2
- = 10 - 10
- = 0

- 10 - 5 x 2

Since the final is 0, 12264 is divisible by 7

*RULE 2:*

- Take the digits of the number in reverse order
- Multiply them successively by the digits 1, 3, 2, 6, 4, 5
- Add the products
- If the resulting sum is divisible by 7, then the original number is divisible by 7

EXAMPLE

Is 12264 divisible by 7 without leaving any remainder?

- Take the digits of the number in reverse order: 46221
- Multiply them successively by the digits 1, 3, 2, 6, 4, 5:.... 4x1, 6x3, 2x2, 2x6, 1x4
- Add the products: 4+18+4+12+4 = 42
- 42 is divisible by 7, so 12264 is also divisible by 7

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