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Finding the Greatest Common Factor (GCF)

Finding the Greatest Common Factor (GCF). Chapter 10.8. What is Factoring?. Factoring is a method to find the numbers and/or variables that make up a product. (Factor) x (Factor) = Product Prime Numbers , have only 2 factors, themselves and 1. Greatest Common Factor (GCF).

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Finding the Greatest Common Factor (GCF)

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  1. Finding the Greatest Common Factor(GCF) Chapter 10.8

  2. What is Factoring? • Factoring is a method to find the numbers and/or variables that make up a product. • (Factor) x (Factor) = Product • Prime Numbers, have only 2 factors, themselves and 1

  3. Greatest Common Factor (GCF) • The Greatest Common Factor (GCF) is the LARGEST FACTOR shared by two or more terms. • ALWAYS try this factoring method 1st before any other method • Divide Out the Biggest common number/variable from each of the terms

  4. Finding the Greatest Common Factor Method #1 – Backwards Distributive Property • Look at each term, see if there is any number that ALL the coefficients can be divided by with no remainder. Write the number outside the parenthesis. • Write any variable that appears in ALL terms outside of the parenthesis. • Raise the variable outside of the parenthesis by the smallest exponent found in your polynomial. YOU NOW HAVE THE GREATEST COMMON FACTOR WRITTEN OUTSIDE OF THE PARENTHSIS. • Divide the polynomial by the GCF, write the quotient inside the parenthesis.

  5. Finding the Greatest Common Factor Method #2 – List and Match • Look at each term of your polynomial on a separate line. • List the prime factors for each term. • Circle the “Matching” factors that appear in each term. • Multiply what you have circled – THIS IS the GCF! Write it outside of the parenthesis. • Multiply what’s “leftover” for each term, write that inside the parenthesis.

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