1. Warm Up 1. 50, 6 2. 105, 7 3. List the factors of 28. Tell whether each number is prime or composite. If the number is composite, write it as the product of two numbers. no yes ±1, ±2, ±4, ±7, Tell whether the second number is a factor of the first number. ±14, ±28 4. 11 5. 98 composite; 49  2 prime

2. Factors and Greatest Common Factors Lesson 8-1

3. Objectives In this lesson you’ll…. Preparation for 11.0 Students apply basic factoring techniques to second- and simple third degree-polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. California Standards

4. Words to know… Factor – a whole number or variable expression that divides evenly into a given whole number or variable expression.Factor – a whole number or variable expression that divides evenly into a given whole number or variable expression. Greatest Common Factor – largest number that divides evenly into a given set of numbers.Greatest Common Factor – largest number that divides evenly into a given set of numbers. Prime factorization- a representation of a number or polynomial as a product of primesPrime factorization- a representation of a number or polynomial as a product of primes

5. Writing Prime Factorization Method 1: Factor tree. 230 2 15 3 5 Method 2: ladder division.

6. You Try: Write the prime factorization of each number 1)202) 36 3)27 4) 545) 1006) 7 22522532223222 3 332332 22522252 7

7. Three ways to find the GCF 1. Make a list of factors. 2. Select common factors from the prime factorizations (or tree diagram). 3. Upside-Down Division

8. Method 1: Make a list of factors. 160 230 320 415 512 610 1 84 4 21 3 28 2 42 6 14 7 12 List all the factor pairs of 60 and 84. What is the greatest factor?

9. You try: Make a list of factors. 114 2727 1 49 7

10. Method 2: Factor Tree Selecting from prime factors. 2 2 30 42 2 15 3 5 21 2 73 What prime numbers do they have in common? GCF = 2 2 3 Or 12

11. You try : Factor Tree Selecting from prime factors. 9 2 8 9 3 4 32 3 3 What prime numbers do they have in common? GCF = 2 3 3 Or 18 2 2

12. Method 3: Upside Down Division GCF = 2 2 3 Or 12

13. You try : Upside Down Division GCF = 2 2 3 Or 12

14. GCF with Expressions GCF = 3m or 3m What prime numbers and variables do they have in common?

15. You try: Find the GCF of the Monomials GCF = 5y or 5y

16. Use any method Practice ~ find the GCF. Use any method 1.2842 2.16 20 3.120140 4.15x²y 12xy³ 5.30a²b 42a³b² 6.14m³n² 21m²n² GCF = 14 GCF = 4 GCF = 20 GCF = 3xy GCF = 6a²b GCF = 7m²n²

17. A few more …(I’m not convinced you know it yet) 1.12 30 2.48 54 3.60130 4. 2x²y10xy² 5. 5r²p³20r³p 6. 36x²y³63x²y³ GCF = 6 GCF = 10 GCF = 2xy GCF = 5r²p GCF = 9x²y³

18. Lesson Quiz: Part I Write the prime factorization of each number. 1. 50 2. 84 Find the GCF of each pair of numbers. 3. 18 and 75 4. 20 and 36 2 2  3  7 2  5 2 4 3

19. Lesson Quiz: Part II Find the GCF each pair of monomials. 5. 12x and 28x 3 6. 27x 2 and 45x 3 y 2 7. Cindi is planting a rectangular flower bed with 40 orange flowers 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? 4x 17 9x29x2