Originally Posted by
topsquark Equation, not that I know of. Process, yes.
Consider the GCF of 60 and 630.
The prime factorization of 60 is $\displaystyle 2^2 \cdot 3 \cdot 5$.
The prime factorization of 630 is $\displaystyle 2 \cdot 3^2 \cdot 5 \cdot 7$.
The GCF (also known as the Greatest Common Divisor, GCD) will be the number that has a prime factorization that contains the same prime factors as the combination of the lists. In other words,
There is a factor of 2 common to each,
there is a factor of 3 common to each,
there is a factor of 5 common to each.
Thus GCF(60, 630) = 2*3*5 = 30.
If we were talking about GCF(60, 1260) then ($\displaystyle 1260 = 2^2 \cdot 3^2 \cdot 5 \cdot 7$):
There are two factors of 2 common to each,
there is a factor of 3 common to each,
there is a factor of 5 common to each.
Thus GCF(60, 1260) = $\displaystyle 2^2 \cdot 3 \cdot 5$ = 60.
-Dan
PS Now that I think of it, there is a formula, but it isn't anything direct:
Given two numbers x and y, we know that GCF(x, y) = (x*y)/LCM(x, y), where LCM(x, y) is the "Least Common Multiple" of x and y. There is no direct formula I know of to find the LCM either.