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Mastering Common Factors in Algebra I

Learn to define and determine the greatest common factor of numbers using factor trees and prime factorization. Practice finding the GCF with helpful examples. Homework includes Section 8.3 problems and a multicultural activity.

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Mastering Common Factors in Algebra I

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  1. COMMON FACTORS Coach Baughman March 16, 2004 Algebra I

  2. COMMON FACTORS • Objectives • The students will define a greatest common factor. (Knowledge) (Mathematics, Algebra I, 4.c) • The students will determine the greatest common factor of numbers. (Analysis) (Mathematics, Algebra I, 4.c)

  3. REVIEW • To factor something means to express it as a product. • Ex: Factors of 18: 1, 18 2, 9 3, 9

  4. COMMON FACTORS • A factor of two or more positive integers is called a common factor of the integers. • The Greatest Common Factor of the given integers is the greatest integer that is a factor of each.

  5. FACTOR TREES AND GCF • We can use our factor trees to find the greatest common factors of numbers. 24 32 2 12 4 8 2 6 2 2 2 4 2 3 2 2

  6. USING PRIME FACTORIZATION TO FIND GCF • It may be easier to find the greatest common factor using prime factorization. 24 = 2 x 2 x 2 x 3 32 = 2 x 2 x 2 x 2 x 2 The GCF of 24 and 32 is (2)(2)(2)=8.

  7. EXAMPLES • Find the GCF of the following numbers: 18 = 2 x 3 x 3 GCF is 9 45 = 3 x 3 x 5 24 = 2 x 2 x 2 x 3 GCF is 12 84 = 2 x 2 x 3 x 7 168 = 2 x 2 x 2 x 3 x 7

  8. EXAMPLES (cont.) • Find the GCF of the following numbers: 28 = 2 x 2 x 7 GCF is 1 75 = 3 x 5 x 5 110 = 2 x 5 x 11 GCF is 1 441 = 3 x 3 x 7 x 7

  9. GREATEST COMMON FACTORS • The last two examples have greatest common factors of 1. Therefore, we say that these numbers are relatively prime.

  10. HOMEWORK • Section 8.3 problems 1, 2, 3, 6, 7 • Multicultural Activity

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