Factoring Out the Greatest Common Factor (GCF)

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In this lesson, we will learn how to factor out the GCF or greatest common factor from a polynomial. Back in pre-algebra, we learned that the greatest common factor for a group of numbers was the largest number that each number of a group was divisible by. When we move into Algebra, we extend this definition to variable terms or monomials (single term polynomials). When we look at a polynomial, we can find the GCF by breaking down each term into its prime factors. We can then make a list of all common prime factors between all terms of the polynomial. Once this is done, we can find the product of everything in our list, and we will have our GCF. To factor the GCF out of a polynomial, we simply write our GCF outside of a set of parentheses and replace each original term with the term divided by the GCF.
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