Divisible by 7
Keith Vetter 2016-04-18 How can you quickly determine if a number is evenly divisible by 7? There are nice tricks for 2, 3, 4, 5, 6, 8 and 9 but 7 is trickier.
Here s a simple, graphical way to test for divisibility by seven. Start at the starred node at the bottom. Now take each digit in turn from left to right in your number. For each digit, follow that many black arrows in a row, and then add one white arrow. If you finish at the bottom, then your number is divisible by 7.
How does it work? Here s a hint: the white arrows correspond to 10x mod 7.