This week, Silvio Moura Velho showed me a new method for determining if a number is divisible by 7 (and by 13). The method is described at: http://www.7and13divisibility.com/. I am impressed at how quickly the method works. What I feel is missing on the site is a good explanation as to why it works. (The "Why it works" tab seems to only provide another example.) Can you explain succinctly why this method works?