GCF of monomials

Learning Objectives Define a monomial and identify its coefficient and variable parts. Find the Greatest Common Factor (GCF) of a set of integers using prime factorization. Identify the GCF of the variable parts of monomials by selecting the lowest power of each common variable. Combine the GCF of the coefficients and the GCF of the variable parts to determine the overall GCF of two or more monomials. Correctly handle cases where a variable is not present in all monomials. Apply the GCF to perform introductory factoring of polynomials by dividing each term by the GCF. Ever tried to organize a big collection of items into the largest possible identical groups? 🤔 That's exactly what we're doing with algebra when we find the GCF! In this tutorial, you will learn how...

TermDefinitionExample MonomialAn algebraic expression consisting of a single term, which can be a number, a variable, or a product of numbers and variables with whole number exponents.7x²y is a monomial. 7x + 2y is not a monomial; it is a binomial. CoefficientThe numerical factor of a monomial.In the monomial -5a³b, the coefficient is -5. FactorA number or monomial that divides another number or monomial evenly, with no remainder.3x is a factor of 12x³ because 12x³ ÷ 3x = 4x². Greatest Common Factor (GCF)The largest monomial that is a factor of two or more given monomials.The GCF of 10x² and 15x is 5x. Prime FactorizationThe process of writing a number as a product of its prime factors.The prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.

GCF of Coefficients Rule GCF(c₁, c₂, ...) To find the GCF of the coefficients, find the largest integer that divides all the numerical coefficients of the monomials. Using prime factorization can be very helpful. GCF of Variables Rule For a variable xⁿ and xᵐ, the GCF is x^min(n,m) For each variable that appears in ALL monomials, choose the term with the lowest exponent. If a variable is not present in all terms, it is not part of the GCF's variable component. Overall GCF of Monomials GCF = (GCF of Coefficients) × (GCF of Variables) The complete GCF of a set of monomials is the product of the GCF of their coefficients and the GCF of their common variable parts.