Factors and Greatest Common Factors 7 1 Common

Factors and Greatest Common Factors 7 -1 Common Factors Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Holt Mc. Dougal

7 -1 Factors and Greatest Common Factors Objectives Write the prime factorization of numbers. Find the GCF of monomials. Holt Mc. Dougal Algebra 1

7 -1 Factors and Greatest Common Factors Example 1: Writing Prime Factorizations Write the prime factorization of 98. Method 1 Factor tree Method 2 Ladder diagram Choose any two factors Choose a prime factor of 98 to begin. Keep finding to begin. Keep dividing by factors until each branch prime factors until the ends in a prime factor. quotient is 1. 98 2 98 7 49 2 49 7 7 1 98 = 2 7 7 The prime factorization of 98 is 2 7 7 or 2 72. Holt Mc. Dougal Algebra 1

7 -1 Factors and Greatest Common Factors Check It Out! Example 1 Write the prime factorization of each number. a. 40 40 2 20 2 10 2 5 40 = 23 5 The prime factorization of 40 is 2 2 2 5 or 23 5. Holt Mc. Dougal Algebra 1 b. 33 11 33 3 33 = 3 11 The prime factorization of 33 is 3 11.

7 -1 Factors and Greatest Common Factors Example 2 A: Finding the GCF of Numbers Find the GCF of each pair of numbers. 100 and 60 Method 1 List the factors of 100: 1, 2, 4, 5, 10, 25, 50, 100 List all the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Circle the GCF. The GCF of 100 and 60 is 20. Holt Mc. Dougal Algebra 1

7 -1 Factors and Greatest Common Factors Example 2 B: Finding the GCF of Numbers Find the GCF of each pair of numbers. 26 and 52 Method 2 Prime factorization. 26 = 2 13 52 = 2 2 13 = 26 Write the prime factorization of each number. Align the common factors. The GCF of 26 and 52 is 26. Holt Mc. Dougal Algebra 1

7 -1 Factors and Greatest Common Factors Check It Out! Example 2 b Find the GCF of each pair of numbers. 15 and 25 Method 2 Prime factorization. 15 = 1 3 5 25 = 1 5 5 1 5=5 Write the prime factorization of each number. Align the common factors. The GCF of 15 and 25 is 5. Holt Mc. Dougal Algebra 1

7 -1 Factors and Greatest Common Factors Example 3 A: Finding the GCF of Monomials Find the GCF of each pair of monomials. 15 x 3 and 9 x 2 15 x 3 = 3 5 x x x 9 x 2 = 3 3 x x 3 Write the prime factorization of each coefficient and write powers as products. Align the common factors. x x = 3 x 2 Find the product of the common factors. The GCF of 15 x 3 and 9 x 2 is 3 x 2. Holt Mc. Dougal Algebra 1

7 -1 Factors and Greatest Common Factors Check It Out! Example 3 a Find the GCF of each pair of monomials. 18 g 2 and 27 g 3 18 g 2 = 2 3 3 27 g 3 = g g Write the prime factorization of each coefficient and write powers as products. 3 3 3 g g g Align the common factors. 3 3 g g Find the product of the common factors. The GCF of 18 g 2 and 27 g 3 is 9 g 2. Holt Mc. Dougal Algebra 1