Equation, not that I know of. Process, yes.

Consider the GCF of 60 and 630.

The prime factorization of 60 is

.

The prime factorization of 630 is

.

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 (

):

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) =

= 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.