This next method is probably beyond the pre-algebra level.  It's really not that bad, but it will seem a bit creepy at first.  I think it's just the name!


The Euclidean Algorithm:

An algorithm is just a list of steps to work through -- like a process where you do the same thing all the time.

I need to show it to you with letters first:

If you want to findGCF( a , b ), you start with

a = qb + r  ...  the q is the quotient  ...  the r is the remainder

In English (haha), you put b into a as many times as it will go (q) and, then, get the remainder.

Here it is with numbers:

  GCF( 16 , 6 )  ...  16 is a  ...  6 is b

1 )  16 = 2 * 6 + 4  ...  6 goes into 16 two times  ...  with 4 left over