8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors
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1 8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1
2 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no , 7 3. List the factors of 28. ±14, ±28 yes ±1, ±2, ±4, ±7, Tell whether each number is prime or composite. If the number is composite, write it as the product of two numbers. 10 pts possible prime composite; pts 2 pts
3 Objectives Write the prime factorization of numbers. Find the GCF of monomials.
4 Vocabulary prime factorization greatest common factor
5 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
6 The order of factors does not change the product, but there is only one example below that cannot be factored further. The circled factorization is the prime factorization because all the factors are prime numbers. The prime factors can be written in any order, and except for changes in the order, there is only one way to write the prime factorization of a number. Factorizations of 12
7 Remember! A prime number has exactly two factors, itself and 1. The number 1 is not prime because it only has one factor.
8 Example 1: Writing Prime Factorizations Write the prime factorization of 98. Factor tree The prime factorization of 98 is or
9 Check It Out! Example 1 Write the prime factorization of each number. a. 40 b. 33 The prime factorization of 40 is or = 3 11 The prime factorization of 33 is 3 11.
10 Check It Out! Example 1 Write the prime factorization of each number. c. 49 d. 19 The prime factorization of 49 is 7 7 or 7 2. The prime factorization of 19 is 1 19.
11 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.
12 Example 2A: Finding the GCF of Numbers Find the GCF of each pair of numbers. 100 and 60 Method 1 List the factors.
13 Example 2B: Finding the GCF of Numbers Find the GCF of each pair of numbers. 26 and 52 Method 2 Prime factorization. Write the prime factorization of each number. Align the common factors.
14 Check It Out! Example 2a Find the GCF of each pair of numbers. 12 and 16
15 Check It Out! Example 2b Find the GCF of each pair of numbers. 15 and 25
16 You can also find the GCF of monomials that include variables. To find the GCF of monomials, write the prime factorization of each coefficient and write all powers of variables as products. Then find the product of the common factors.
17 Example 3A: Finding the GCF of Monomials Find the GCF of each pair of monomials. 15x 3 and 9x 2 Write the prime factorization of each coefficient and write powers as products. Align the common factors. The GCF of 3x 3 and 6x 2 is 3x 2. Find the product of the common factors.
18 Example 3B: Finding the GCF of Monomials Find the GCF of each pair of monomials. 8x 2 and 7y 3 The GCF 8x 2 and 7y is 1. Write the prime factorization of each coefficient and write powers as products. Align the common factors. There are no common factors other than 1.
19 Helpful Hint If two terms contain the same variable raised to different powers, the GCF will contain that variable raised to the lower power.
20 Check It Out! Example 3a Find the GCF of each pair of monomials. 18g 2 and 27g 3 Write the prime factorization of each coefficient and write powers as products. Align the common factors. The GCF of 18g 2 and 27g 3 is 9g 2. Find the product of the common factors.
21 Check It Out! Example 3b Find the GCF of each pair of monomials. 16a 6 and 9b Write the prime factorization of each coefficient and write powers as products. The GCF of 16a 6 and 7b is 1. Align the common factors. There are no common factors other than 1.
22 Check It Out! Example 3c Find the GCF of each pair of monomials. 8x and 7v 2 Write the prime factorization of each coefficient and write powers as products. Align the common factors. The GCF of 8x and 7v 2 is 1. There are no common factors other than 1.
23 HOMEWORK Section 8-1 (page 527) 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 38, 40, 41, 42, 48, 49, 50, 51, 53, 69-71
24 HOMEWORK
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