7 1 Factors and Greatest Common Factors Objectives
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 Vocabulary prime factorization greatest common factor Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors The whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. You can use the factors of a number to write the number as a product. The number 12 can be factored several ways. Factorizations of 12 Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors Remember! A prime number has exactly two factors, itself and 1. The number 1 is not prime because it only has one factor. 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 Check It Out! Example 1 Write the prime factorization of each number. c. 49 d. 19 49 7 7 49 = 7 7 The prime factorization of 49 is 7 7 or 72. Holt Mc. Dougal Algebra 1 1 19 19 19 = 1 19 The prime factorization of 19 is 1 19.
7 -1 Factors and Greatest Common Factors that are shared by two or more whole numbers are called common factors. The greatest of these common factors is called the greatest common factor, or GCF. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 32: 1, 2, 4, 8, 16, 32 Common factors: 1, 2, 4 The greatest of the common factors is 4. Holt Mc. Dougal Algebra 1
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 a Find the GCF of each pair of numbers. 12 and 16 Method 1 List the factors of 12: 1, 2, 3, 4, 6, 12 List all the factors of 16: 1, 2, 4, 8, 16 Circle the GCF. The GCF of 12 and 16 is 4. 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 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 Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors Example 3 B: Finding the GCF of Monomials Find the GCF of each pair of monomials. 8 x 2 and 7 y 3 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 Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors Check It Out! Example 3 b Find the GCF of each pair of monomials. 16 a 6 and 9 b Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors Check It Out! Example 3 c Find the GCF of each pair of monomials. 8 x and 7 v 2 Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors Lesson Quiz: Part I Write the prime factorization of each number. 1. 50 2 52 2. 84 22 3 7 Find the GCF of each pair of numbers. 3. 18 and 75 3 4. 20 and 36 4 Holt Mc. Dougal Algebra 1
7 -1 Factors and Greatest Common Factors Lesson Quiz: Part II Find the GCF of each pair of monomials. 5. 12 x and 28 x 3 4 x 6. 27 x 2 and 45 x 3 y 2 9 x 2 7. Cindi is planting a rectangular flower bed with 40 orange flower and 28 yellow flowers. She wants to plant them so that each row will have the same number of plants but of only one color. How many rows will Cindi need if she puts the greatest possible number of plants in each row? 17 Holt Mc. Dougal Algebra 1
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