All non-prime integers (composite numbers or integers) can be broken down into factors. Fractions are formed when two integers are arranged into a fraction: a/b, where a and b are different integers. If a and b are composite integers, they can each be replaced by the product of their factors. If they have a common factor, that factor can be used to reduce the fraction to a simpler form. The greatest common factor is the largest of the common factors, which is the product of all the common prime factors (prime means that the factor cannot be reduced further). The GCF is also useful in ratios as a means of simplifying the ratio. So GCF only applies if there are two or more integers. Example: 420 and 378. 420=2*2*3*5*7 and 378=2*3*3*3*7. These numbers have three factors in common: 2, 3 and 7. If we multiply them together we get 2*3*7=42. This is the GCF. If we saw the fraction: 378/420 we can reduce it by dividing top and bottom by 42 to get 9/10. Example: 24:84:144 can be reduced to 2:7:12 by dividing each number by the GCF 12.