Explore the fascinating world of prime factorization in this 42-minute video lecture from the "Famous Math Problems" series. Delve into the challenge of factoring an incredibly large number into its prime components. Learn about the Fundamental Theorem of Arithmetic, modular arithmetic, and the theorems of Fermat and Euler. Discover practical applications using Wolfram Alpha and tackle division exercises to reinforce your understanding. Gain insights into the complexities of working with big numbers and the importance of prime factorization in mathematics.