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Greatest Common Factor (GCF)

Greatest Common Factor (GCF). Definitions:. Common Factor : A whole # that is a factor of two or more whole #’s. Ex: 1, 2, 3, and 6 are common factors of 12 and 18.

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Greatest Common Factor (GCF)

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  1. Greatest Common Factor (GCF)

  2. Definitions: • Common Factor: A whole # that is a factor of two or more whole #’s. Ex: 1, 2, 3, and 6 are common factors of 12 and 18. • Greatest Common Factor (GCF): The largest common factor of the #’s. (Sometimes called the Greatest Common Devisor (GCD)). Ex: 6 is the GCF of 12 and 18.

  3. Using a list to find the GCF (Best for small #’s) Ex: Find the GCF of 16 and 20 16: 1, 2, 4, 8, 16 20: 1, 2, 4, 5, 10, 20 Common Factors: 1, 2, 4 GCF: 4

  4. Using Prime Factorization to find the GCF:(Best for large #’s) Ex: Find the GCF of 180 and 378. 180 2 • 90 2 • 45 3 • 15 3 • 5 = 2•2•3•3•5 378 2• 189 3 • 63 3 • 21 3 • 7 = 2•3•3•3•7 Common Factors: 2•3•3 = 18 GCF = 18

  5. Least Common Multiple (LCM)

  6. Definitions: • Multiple: A product of the # and any nonzero whole #. • Common Multiple: A multiple shared by two or more #’s • Least Common Multiple: The smallest common multiple shared by two or more #’s.

  7. Using a list to find the LCM: • Find the LCM of 6 and 9. 6: 6, 12, 18, 24, 30, … 9: 9, 18, 27, 36, 45, … The LCM is 18.

  8. Using Prime Factorization to find the LCM: • Find the LCM of 180 and 378. 180 378 Recall from GCF notes we know the prime factorization: 2 ● 3 ● 3 ● 3 ● 7 2 ● 2 ● 3 ● 3 ● 5 2•3³•7 2²•3²•5 Now compare each factor in the exponential form. Write down which is LARGER. 2²•3³•5•7= 3780

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