Rotations of a number

This is a direct implementation of this answer https://math.stackexchange.com/a/1967330/92921

m = 308460277;
Reap[NestWhile[{#[[1]] - #[[2]] Sow@Floor[Divide @@ #]], 
      Floor[#[[2]]/10]} &, {m, 
     FromDigits@ConstantArray[1, Ceiling@Log[10, m]]} , #[[2]] > 
      0 &]][[2, 1]] // FromDigits

277614253

note this gives the 'closest' value for any input m. You need to check that its correct:

 Total@NestWhileList[ Floor[#/10] &, 277614253, # > 0 &]==m

True

I'm not sure of the etiquette re: reposting here vs giving code answers on the math site..

A ploddingly procedural implementation:

n = 308460277;
FromDigits[Reap[Do[{q, n} = QuotientRemainder[n, (10^k - 1)/9]; Sow[q],
                   {k, IntegerLength[n], 1, -1}]][[-1, 1]]]
   277614253