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How Do You Find the Greatest Common Factor of Monomials?

Find the greatest common factor between the four monomials shown on the right.

Summary

  1. GCF stands for greatest common factor
  2. To find the GCF we need to factor each monomial as much as possible
  3. Circle the common factors that are in each monomial
  4. The common factors of the monomials are 2, x, and y
  5. The GCF is just the product of the three common factors

Notes

    1. We're factoring the first monomial
    1. We're factoring the second monomial
    1. We're factoring the third monomial
    1. We're factoring the last monomial
    1. The greatest common factor will be the product of the common factors in each monomial
    1. Our greatest common factor will be the product of the common factors in each monomial
    1. We can circle 2 since occurs in each factorization
    1. 3 is neither in the second nor in the fourth factorization, so it is not a common factor to all four
    1. This means that 3 is not a common factor of all four monomials
    1. There is at least one 'x' in each monomial!
    1. There is at least one 'y' in each monomial!
    1. The greatest common factor will be the product of the common factors in each monomial
    1. The circled numbers are the common factors that are in each monomial
    1. The greatest common factor is the product of the common factors in each monomial
    1. GCF stands for greatest common factor
    1. GCF stands for greatest common factor
    1. GCF stands for greatest common factor