Puzzle of the Week #70 - Divisibility Test

It is easy to test a number for divisibility by 2, 5 or 10, by just looking at the final digit. Divisibility by 3 or 9 is almost as easy, whereby you add together the digits of your number, and if the resulting total (which will necessarily be smaller than your original number) is divisible by 3 (or 9), then so was your original number.

But can you devise a test for divisibility by 7, 11 or 13 (the same procedure for all three) where you can very simply, using addition and subtraction, reduce a number of however many digits, down to a three digit number, which will be divisible by 7, 11 or 13, if and only if your original number was?