Thanks to my supporters on Patreon! Get early access to videos and more: Why can a natural number only be factored in one way as a product of primes? Surprisingly, it comes down to the world's oldest algorithm -- the Euclidean algorithm -- which computes the gcd of two numbers. #SoME4 ---------------- Reference: :// ---------------- 0:00 Destroying laptops 0:56 RSA-100 1:40 Unique factorization 2:45 Applications 3:27 Most important fact 4:02 Idea behind the Euclidean algorithm 5:31 Euclidean algorithm 7:02 Why factorization is unique 9:30 Euclid's lemma 14:18 Extended Euclidean algorithm 16:49 Proof of Euclid's lemma 17:46 Fibonacci numbers ---------------- Animated with Manim. Music by Callistio. Web site: