Someone wrote "The algorithm that Cooley and Tukey presented in their classic paper (Math. Comp. 19 (1965), 297-301. http://dx.doi.org/10.1090/S0025-5718-1965-0178586-1) can be applied to any composite length. The performance advantages are greatest for highly composite lengths, of which powers-of-2 are one example, and lengths of powers-of-2 result in other advantages on binary computers, so it has become a common misconception that the algorithm is only applicable to signals whose length is a power of 2."
Does that mean that when you DO use the Cooley-Tukey FFT You don't have to zeropad to a power of 2? Take for example an image of 1920x1080. So, if you want to use the Cooley-Tukey FFT, you don't need to zeropad that to 2048*2048?