Euclidean Algorithm and Jug Filling (VIDEO!)

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.

Jug Filling


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


  • Books

  • Get in touch