Yes, it was the 1/N factor I was remembering or not remembering as the case may be. Like I said, when I was introduced to this part of DSP, it was given that 1/N is known to be needed to "close the loop", but there is no rational for where you include it.
As to the other conversion factors, yes, they are there, but that is just a matter of the quantization levels established by the A to D conversion process. As John mentions, there are also factors that need to be included for any windowing function used. Is there something else that needs to be considered? I've never taken a known sine wave an performed an FFT on it to calibrate the process. I should try that when I get some time.