Dividing by 7

[Zzzptm]

Had a very interesting dream in which I presented myself with the problem of solving 260 divided by 224. I reduced it to 65/56 in my dream and got the first few digits of the decimal approximation, but had to wake up to resolve the repeating part.

Now I find myself intrigued with how numbers look when they've been divided by 7 or by a number with 7 as one of its factors. It can be resolved by choosing one factor of the number over 7 multiplied by whatever else the other factors resolve to, with the 142857 repeating portion coming in at the end, starting on whichever number is appropriate for the factor/7 selected.

I determined that the repeating decimal initial number can be found with a bit of modulo math. If the factor equals 1 more than a multiple of 7, it will be 142857. 2 more, it will be 285714. 3 more, 428571. 4 more, 571428. 5 more 714285. 6 more 857142. (Easy to type on a numpad, as no 3, 6, 9, or 0 needed in that pattern.)