More seriously, if you consider that the series 10^0, 10^1, 10^2, 10^3, etc. in modulo 7 runs as 1, 3, 2, -1, -3, -2, (loop with period 6), the remainder upon d

More seriously, if you consider that the series 10^0, 10^1, 10^2, 10^3, etc. in modulo 7 runs as 1, 3, 2, -1, -3, -2, (loop with period 6), the remainder upon dividing a decimal number FEDCBA by 7 = the remainder on dividing (A-D) + 3(B-E) + 2(C-F) by 7. Ex: 23456 mod 7 = 3+9+8 mod 7 = 6