Sure, I know full well you’re actually doing modular arithmetic. But if you don’t tell people, they won’t get frightened. If you’re going to mention it, mention it afterward.

7 is going to be an issue precisely because the decimal expansion of 1/7 has the longest possible period for its size, 6. (Performing the division for non-terminating 1/N can at most go through the N -1 possible non-zero remainders).

The periodicity of the decimal expansion of 1/N is a non-trivial problem that you can have a lot of fun playing with.

I learned this all from Martin Gardner’s Scientific American columns, mostly as collected into books. If you love recreational mathematics, these are still golden.