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OBJECTIVES: • find the Greatest Common Factor of two or more numbers or monomials • use the Distributive Property to factor algebraic expressions Warm up: p. 163 Section 44 ________________ "Practice Quiz 1" Venn diagram 20 12 The Venn diagram on the right shows the prime factors of 12 and 20. The common prime factors are in both circles. 2 3 2 5 a. Which numbers are in both circles? b. Find the product of the numbers that are in both circles. c. Is the product also a factor of 12 and 20? Greatest Common Factor Example 2: Find the GCF of each set of numbers. a. 30 and 24 b. 54, 36, 45 Example 1: Find the GCF of 12 and 20 Step 1: Write as prime factors Step 2: Circle the ones that are the same Step 3: Multiply the common primes from one row 12 = 2 2 3 20 = 2 2 5 GCF = 1 Example 3: There are 208 boys and 240 girls participating in a field day competition. Example 4: Find the GCF of the monomials. 16xy2 and 30xy a. What is the greatest number of teams that can be formed if each team has the same number of girls and the same number of boys? b. How many boys and girls will be on each team? Example 5: Factor 2x + 6 Guided Practice: Step 1: Find the GCF of the terms Step 2: Write each term as a product of the GCF and other factors. Step 3: Use the reverse of the Distributive Property. 1. Find the error. Christina and Jack both found the GCf of 2 32 11 and 23 5 11. Who is correct? Why? Christina Jack 2 33 11 2 32 11 23 5 11 2 2 2 5 11 GCF = 11 GCF = 2 11 = 22 2 Find the GCF of each set of numbers or monomials. 2. 6 and 8 3. 21, 45 4. 16, 56 5. 28, 42 Factor each expression. 10. 3n + 9 11. t2 + 4t 12. 15 + 20x 13. 4y 16 6. 7, 30 7. 108, 144 8. 14n, 42 n2 9. 36a3b, 56ab2 14. In the parade, 36 members of the color guard are to march in front of 120 members of the marching band. Both groups are to have the same number of students in each row. Find the greatest number of students in each row. 3 Do you have any Vocab questions? OBJECTIVES: HOMEWORK: p. 167 168 # 18 54 even, 59, 60 4