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Euclidean Algorithm to Find the GCD of Two Numbers | Why Does It Work?

The Euclidean Algorithm is used to find the greatest common divisor of two whole numbers. We recursively use the Division Algorithm to find GCD(1224,567) as the last nonzero remainder. Why does it work? "Friendly Introduction to Number Theory": https://amzn.to/3Ixo9Lq 🔴 "Foundations of Arithmetic, Algebra, and Graphing" playlist:    • Foundations of Arithmetic, Algebra, a...   🔴 Abstract Algebra Course Lectures playlist:    • Abstract (Modern) Algebra Course Lect...   🔴 Ultimate AP Calculus AB Review:    • Ultimate AP Calculus AB Review   The greatest common divisor GCD is also known as the greatest common factor GCF or highest common factor HCF. Check the answer with factor trees. #number #numbers #gcd Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ (0:00) Euclidean Algorithm problem and description in terms of the Division Algorithm (0:33) Use Euclidean Algorithm to find GCD(1224,567) (1:58) Check answer with factor trees (3:28) Why does it work? AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.