In music, the fundamental frequency $f_0$ is the gcd of the frequencies $f_n$ of the harmonics. Find the fundamental frequency $f_0$ of the harmonics:
$f_1$ = 200Hz, $f_2$ = 300Hz, $f_3$ = 400Hz, and $f_4$ = 500Hz.
The factors of each frequency are as follows:
- Factors of 200 are $\{1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200\}$
- Factors of 300 are $\{1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300\}$
- Factors of 400 are $\{1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400\}$
- Factors of 500 are $\{1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500\}$
The gcd is 100, and so the fundamental frequency $f_0$ is 100Hz.