By the prime factorization theorem, every integer can be uniquely
factored into a product of prime numbers raised to an
integer power :

As discussed above, a mixed-radix Cooley Tukey FFT can be used to
implement a length DFT using DFTs of length . However, for
factors of that are mutually prime (such as and
for ), a more efficient prime factor
algorithm (PFA), also called the Good-Thomas FFT algorithm,
can be used [24,78,81].^{A.5}The Chinese Remainder
Theorem
is used to re-index either the input or output samples for the PFA.^{A.6}Since the PFA is only applicable to mutually prime factors of , it
is ideally combined with a mixed-radix Cooley-Tukey FFT, which works
for any integer factors.

It is interesting to note that the PFA actually predates the
Cooley-Tukey FFT paper of 1965 [14], with Good's
1958 work on the PFA being cited in that paper [81].