Greatest common factor

Learning Objectives Define the Greatest Common Factor (GCF) for integers, monomials, and polynomials. Determine the GCF of two or more integers using the prime factorization method. Find the GCF of two or more algebraic monomials. Identify the GCF of the terms in a polynomial. Factor a polynomial by extracting its GCF. Apply the concept of GCF as the first step in more complex factoring problems. Ever tried to create identical goodie bags for a party with different amounts of candy? 🤔 The GCF is your secret tool to find the maximum number of bags you can make! This tutorial will guide you through understanding and finding the Greatest Common Factor (GCF). Mastering the GCF is a critical first step for factoring polynomials, simplifying expressions, and solving quadratic eq...

TermDefinitionExample FactorA number or algebraic expression that divides another number or expression evenly, with no remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 3x² are 1, 3, x, x², 3x, and 3x². Common FactorA factor that is shared by two or more numbers or expressions.The numbers 12 and 18 share the common factors 1, 2, 3, and 6. Greatest Common Factor (GCF)The largest factor that is shared by two or more numbers or expressions. It is the product of all common prime factors raised to their lowest powers.For 12 and 18, the GCF is 6. For 4x²y and 6xy, the GCF is 2xy. Prime FactorizationThe process of breaking down a number into a product of its prime factors.The prime factorization of 60 is 2 × 2 × 3 × 5, or 2² × 3 × 5. MonomialAn algebraic expression consisting...

Prime Factorization Method for GCF GCF = Product of common prime factors, each raised to its lowest power. This is the most reliable method for finding the GCF of integers and algebraic terms. First, find the prime factorization of each number or expression. Then, identify all the prime factors they have in common and multiply them together, using the smallest exponent for each common factor. GCF of Monomials GCF(ax^m, bx^n) = GCF(a, b) \cdot x^{\min(m, n)} To find the GCF of two or more monomials, find the GCF of the numerical coefficients. Then, for each variable that appears in all monomials, take the one with the lowest exponent. Multiply the GCF of the coefficients and the variable parts together. Factoring Polynomials using GCF P(x) = GCF \cdot (\frac{\text{term}...