What is the number theory for figurng out what is divisible by 7?

First of all, it is the one that is probably not even worth doing. It is honestly easier in most cases to just try it! 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.