Sorry, but I think I am missing something here.
If you have 123456789 / 1234 then n=4
first step is r{5} = 12345, ignore n-1=12 for dividend and 1 for divisor.
So, it is fair to say that you always divide the first 2 digits of the dividend by the first digit of the divisor, (and then add the remainders are you did)

If not, can you give another example where the x/y would give a greater number.

Also, you have a type, q = 56 / 8 = 7, not 8 as you have it in your example.