> Long division makes my head hurt!

Well, I suspect it has something to do with writing out the process of 5772 / 37 as

         156
       ______
    37 | 5772
         37
         ---
         207
         185
         ----
          222
          222
          ---
            0

because it a) reverses the order of dividend and divisor for no good reason; b) the result goes up instead of to the right or down. Why not write it like this

    5772 | 37 
    37   +----
    ---    156
    207
    185
    ----
     222
     222
     ---
       0

instead? In fact, I think we could replace the corner with just normal slash, "/", write = to the right of the divisor and spell out the digits of the result to the right of it; the substraction chain will still go down the page.