# Euclidean Algorithm

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Euclidean Algorithm
How do you find the greatest common factors of two numbers? Ask Euclid! Here we demonstrate and explain the famous Euclidean algorithm

Are Factor Trees Unique?
Most assume it is “obvious” that all factor trees of the same number lead to the same list of primes at the end - no matter the choices one makes along the way in making the tree. Well … Let me share with you what the school children of Evenastan know!

Euclidean Algorithm and Jug Filling
Given a 3-gallon jug and a 5-gallon jug, how does one obtain exactly one gallon of water? Jug Filling problems play a key role in the foundation of number theory, in particular, in proving the Fundamental Theorem of Arithmetic (all factor trees lead to the same set of primes). Here’s a brief introduction to Euclid’s continued brilliance on the topic of numbers.

Fundamental Theorem of Arithmetic: Proof!
Following the video that questions the uniqueness of factor trees, the video on the Euclidean Algorithm, and the video on Jug Filling, we are now, finally, in a position to prove the Fundamental Theorem of Arithmetic. Euclid’s brilliance shines on!

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