To determine if a number is divisible by 7, take the last digit off the number, double it and subtract the doubled number from the remaining number. If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.), then the number is divisible by seven. This may need to be repeated several times.

Example: Is 3101 evenly divisible by 7?

 310   - take off the last digit of the number which was 1
  -2   - double the removed digit and subtract it
 308   - repeat the process by taking off the 8
-16    - and doubling it to get 16 which is subtracted
 14    - the result is 14 which is a multiple of 7