To view the notebooks you'll need the LiveMath plug-in, found at
http://www.livemath.com/plugin/

Euclid's Method and its Generalization

Choose two distinct positive integers for a and b, below. Highlight the right-hand side
and type your choice. The steps of the classical Euclidean algorithm for finding the
greatest common divisor (GCD) of a and b are displayed. To see that you might need all
the room provided, try a = 6557470319842 and b = 4052739537881. The actual steps of
Euclid's method are not as important as an expression for the GCD in terms of your two
numbers a and b. Scroll down to see this.

No support for LM Objects

The GCD can be expressed in terms of a and b in infinitely many ways, two of which are shown
below. Here, your choice of a and b cannot be quite as large as in the demonstration, above,
where all the steps are shown. Experiment to see what is possible. If question marks appear,
exchange the values of  a and b.

No support for LM Objects


Original mathematical design © 2003 by Dean Clark