I've loved this visualization for Euclid's Algorithm since the first time I saw it... which might have been at NRICH. [url]http://nrich.maths.org/1357[/url]
To me, the rectangle visualization helps to understand what is going on, why the algorithm works, why the quotients and remainders are significant.
In this visualization you can also see how robust the algorithm is, and how quickly it converges to greatest common divisor.
Note that occasionally one of the sets of squares disappears, for no reason that I can find! Try another number or reset the sketch.
