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9.1 Factors and Greatest Common Factors Part 2 Objective: To be able to find the greatest common factor of monomials. Objective: To be able to find the greatest common factor of monomials.

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GCF The greatest common factor is the greatest number that is a factor of both original numbers. Hint: The GCF of two or more monomials is the product of the prime factors common to the integers.

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Relatively Prime If two or more monomials have a GCF of 1, then they are said to be relatively prime. Give an example of two integers that are relatively prime.

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Steps: List the prime factorization of each term horizontally. **Use the FACTOR TREE** Circle each number or variable that all of the terms have in common. Copy down each number or variable ONCE. Multiply what you have. That is the GCF. How to Use Prime Factorization to find the GCF of Two Monomials:

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Example 1 Find the GCF of each monomial using prime factorization. a.24 and 36

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Example 1 Find the GCF of each monomial using prime factorization. b.54, 63, and 180

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Example 2 Find the GCF of each monomial using prime factorization. a.36x 2 y and 54xy 2 z

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Example 2 Find the GCF of each monomial using prime factorization. b.12a 2 b and 90a 2 b 2 c

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Example 2 Find the GCF of each monomial using prime factorization. c.24gh and 36g 2 h 2

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Classwork TB p. 478 #48 – 60 even

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Homework TB p. 478 #49 – 61 odd

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