More Lessons for Math Trivia

Math Worksheets

Euclidean Algorithm

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

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!

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.

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!

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.