How to compute fundamental frequency from a list of overtones?

Given a list of overtones (F1, F2, F3, etc), how do I compute the fundamental frequency? Can I do something like F2/F1=F1/F0? Is it the correct method to use?

Answer

The frequencies of the harmonics are integer multiples of the fundamental frequency $f_0$, i.e. $f_n = (n+1)f_0$. The fundamental frequency $f_0$ is the greatest common divisor of the harmonics $f_n$. If you are sure that there is no other unknown harmonic between two known harmonics, e.g. you know that you have the fourth and the fifth harmonic, then $f_0$ is of course the difference between the two. But if you just have a collection of harmonics and you don't know anything else about them, then you need to determine $f_0$ as the gcd of $f_n$.