Here's another human-friendly scheme to test divisibility by 7 that I don't think is popularly known: Write down the number, then cross off the least significant digit, double it, and subtract that from what's left of the number. Repeat until you get zero or an obviously divisible-by-7 number, or not.
Example: 325 becomes 32 - 10 = 22, which is obviously not divisibile by 7.
Better example: 8638 -> 863 - 16 = 847 -> 84 - 14 = 70 -> 7 - 0 -> 7, so we have a winner.
Learned this as a kid (forget where), but it took decades for me to realize why it obviously works.
Example: 325 becomes 32 - 10 = 22, which is obviously not divisibile by 7.
Better example: 8638 -> 863 - 16 = 847 -> 84 - 14 = 70 -> 7 - 0 -> 7, so we have a winner.
Learned this as a kid (forget where), but it took decades for me to realize why it obviously works.