Largest possible downsampling factor With the intention of converting a single rate LPF FIR filter to multi rate equivalent: what is the largest possible downsampling factor? I found one source that said it was the sampling frequency divided by the frequency at the centre of the transition band, but am seeking verification.
There is not one correct answer to this question, other than the theoretical one which would be that the maximum downsampling factor $M$ is given by

$$M=\frac{f_s}{f_c}$$

where $f_c$ is the highest frequency of the (ideally band-limited) signal. Since there's no ideally band-limited signal, it depends on the application how much aliasing can be tolerated. The frequency $f_c$ must be chosen as the frequency above which the signal (after low pass filtering) has no significant energy. What 'significant' means is determined by the application.