In math 347 I learned a nice example to finding the gcd for two numbers. It was done in terms of tiling a rectangular floor. The goal is to tile a rectangular room with square tiles of equal dimensions. Thus we want to find the largest size square tile that will exhaust the floor and will leave no remainder.

The basic process is to subtract inscribed squares away from our rectangle until there is no remainder. Then, when you finally get to the point where all that's left are squares with no rectangular remainders, you have found what size tile is required to completely tile the floor. The length of the side of the tile you found is the gcd of the length of the sides of the rectangular room.

Its kind of tough to understand without an illustration. Check out this article: http://www.jstor.org/pss/3617041

It illustrates exactly what I mean to describe. I hope ya find this useful.

This is basically an illustrated Euclidean Algorithm.