Could this be the foundation of Number Theory? The Euclidean Algorithm visualized

The Euclidean Algorithm might just be the most fundamental idea in all of Number Theory. In this video I introduce the Euclidean Algorithm, taking inspiration from Martin H. Weissman's An Illustrated Theory of Numbers.

You can find Martin's book here:
http://illustratedtheoryofnumbers.com/

Thank you to Grant Sanderson of 3blue1brown and the manim community for developing manim, the mathematical animation library that I used to make this video.

This video is also my entry into Grant's SoME contest. You can find more info about that here:
   • Make math videos! | Summer of Math Ex...  

Answer to (1). Definition of the GCD:
A number g is called the "greatest common division" of a and b if it satisfies the following two properties
1) g is a "common divisor" of a and b. In other words, g divides a and g divides b.
2) If d is a common divisor of a and b, then d divides g.

Note that this definition doesn't use the order of the natural numbers (less than, greater than or equal to symbols) but only the property of divisibility.

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