So what? Being a prime number doesn’t mean it can’t be a divisor. Or is it the string of 9s that’s supposed to be upsetting? Why? What difference does it make?

⅐ = 0.1̅4̅2̅8̅5̅7̅

The above is 42857 * 7, but you also get interesting numbers for other subsets:

     7 * 7 =     49
    57 * 7 =    399
   857 * 7 =   5999
  2857 * 7 =  19999
 42857 * 7 = 299999
142857 * 7 = 999999

Related to cyclic numbers:

142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
142857 * 7 = 999999

The divisability rule for 7 is that the difference of doubled last digit of a number and the remaining part of that number is divisible by 7.

E.g. 299’999 → 29’999 - 18 = 29’981 → 2’998 - 2 = 2’996 → 299 - 12 = 287 → 28 - 14 = 14 → 14 mod 7 = 0.

It’s a very nasty divisibility rule. The one for 13 works in the same way, but instead of multiplying by 2, you multiply by 4. There are actually a couple of well-known rules for that, but these are the easiest to remember IMO.

42857 for those who wonder

And for ops title: 23076923