How to Find the Greatest Common Factor of Monomials

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step tutorial on how to find the Greatest Common Factor (GCF) of multiple monomials. The instructor builds upon previous knowledge of factoring single monomials to demonstrate how to identify the largest numerical factor and the highest degree variable shared across a set of terms. The video uses a visual "complete factorization" method where numbers are broken down into primes and variables are fully expanded to make the common elements obvious. The video explores key algebraic themes including prime factorization, laws of exponents, and the structure of monomials. It emphasizes the definition of GCF in this context as the "biggest and highest degree monomial" that can divide into all given terms without leaving a remainder. The instructor works through two distinct examples involving different coefficients and variables (x and d) to reinforce the process. For educators, this video serves as an excellent instructional tool for introducing factoring in Algebra 1. It bridges the gap between basic arithmetic GCF and algebraic factoring, preparing students for the more complex task of factoring polynomials. The visual method of expanding variables (e.g., writing x^3 as x*x*x) is particularly helpful for visual learners and students who struggle with abstract exponent rules, making the logic behind identifying common variables concrete and tangible.