How do you find the greatest common factor of fractions?

You don't. The highest common factor, also called the greatest common divisor, is a feature of whole numbers (also known as integers).
The highest common factor (hcf) of two numbers is the biggest whole number that divides exactly into both.
As an example, the hcf of 48 and 80 is 16 as 48 is 3x16 and 80=5x16.

However, if you do have a fraction such as 60/90 where the top and bottom are whole numbers with a highest common factor bigger than 1, in this case 30, then dividing top and bottom by it will give the fraction in its lowest terms (2/3).

thanks!