1. 4-1 Factors and Prime Factorization Do Now Do Now Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 4-1 Factors and Prime Factorization Do Now – In your notebook Identify each number as prime or composite. 1. 192. 82 3. 574. 85 5. 1016. 121 prime composite prime

3. 4-1 Factors and Prime Factorization SWABAT write prime factorizations of composite numbers. Objective:

4. 4-1 Factors and Prime Factorization Vocabulary Factor prime factorization Greatest common factor (GCF)

5. 4-1 Factors and Prime Factorization Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. 23 6 = Factors Product 2 63 ÷ = 6÷2 = 3 6 is divisible by 3 and 2. We can think of factors as the smaller numbers that multiply to give us the original number.

6. 4-1 Factors and Prime Factorization When the pairs of factors begin to repeat, then you have found all of the factors of the number you are factoring. Helpful Hint

7. 4-1 Factors and Prime Factorization Example 1 List all of the factors of the number 16. 16 16 = 1 16 16 = 2 8 1 2 16 = 4 4 3 4 5 6 7 16 = 8 2 8 The factors of 16 are 1, 2, 4, 8, and 16. 1244168 You can draw a diagram to illustrate the factor pairs. is a factor. is not a factor. is a factor. is not a factor. and 2 have already been listed so stop here.

8. 4-1 Factors and Prime Factorization Example 2 List all of the factors of the number 19. 19 19 = 1 1919 is not divisible by any other whole number. The factors of 19 are 1 and 19.

9. 4-1 Factors and Prime Factorization Example 3 List all of the factors of the number 12. 12

10. 4-1 Factors and Prime Factorization Example 4 List all of the factors of the number 11. 11

11. 4-1 Factors and Prime Factorization You can use factors to write a number in different ways. Factorization of 12 2 61 123 43 2 2 The prime factorization of a number is the number written as the product of its prime factors. Notice that these factors are all prime.

12. 4-1 Factors and Prime Factorization You can use exponents to write prime factorizations. Remember that an exponent tells you how many times the base is a factor. Helpful Hint

13. 4-1 Factors and Prime Factorization Example 5 Method 1: Use a factor tree. Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor. 24 212 6 2 2 3 24 6 4 322 2 24 = 2 2 2 3 24 = 3 2 2 2 The prime factorization of 24 is 2 2 2 3, or 2 3 3. Write the prime factorization of 24.

14. 4-1 Factors and Prime Factorization In Example 5, notice that the prime factors may be written in a different order, but they are still the same factors. Except for changes in the order, there is only one way to write the prime factorization of a number.

15. 4-1 Factors and Prime Factorization Example 6 Write the prime factorization of 28. Method 1: Use a factor tree. Choose any two factors of 28 to begin. Keep finding factors until each branch ends at a prime factor. 28 214 72 28 7 4 2 2 28 = 2 2 7 28 = 7 2 2 The prime factorization of 28 is 2 2 7, or 2 2 7.

16. 4-1 Factors and Prime Factorization Communicator Activity 445642 39 3612585

17. 4-1 Factors and Prime Factorization Do Now List all the factors of each number. 1. 22 2. 40 3. 51 1, 2, 4, 5, 8, 10, 20, 40 1, 2, 11, 22 1, 3, 17, 51 Write the prime factorization of each number. 4. 32 5. 120 2525 2 3  3  5

18. 4-1 Factors and Prime Factorization SWBAT find the greatest common factor (GCF) of a set of numbers. Objective:

19. 4-1 Factors and Prime Factorization Victoria earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? Question of the Day Partner Activity

20. 4-2 Greatest Common Factor Factors shared by two or more whole numbers are called common factors. The largest of the common factors is called the greatest common factor, or GCF. Factors of 18: Factors of 24: Common factors: 1,2,3,4,6, 8, 1, 2, 3, 6 The greatest common factor (GCF) of 18 and 24 is 6. 1, 2,3,6, 9, 12, 18 24 There are several ways to find the greatest common factor. This method is called the “listing method”.

21. 4-2 Greatest Common Factor Example 1: Finding the GCF Find the GCF of the set of numbers. 28 and 42 Method 1: List the factors. factors of 28: factors of 42: 1,2,14,7,28 7,1, 4, 3,2,426,21,14, List all the factors. Circle the GCF. The GCF of 28 and 42 is 14.

22. 4-2 Greatest Common Factor TOYO Find the GCF of the set of numbers. 18 and 36 Method 1: List the factors. factors of 18: factors of 36: The GCF of 18 and 36 is 18.

23. 4-2 Greatest Common Factor Do Now Find the GCF of the set of numbers using the listing method. 1.) 16 and 282.) 24 and 36

24. 4-2 Greatest Common Factor Homework – pg. 153, #’s 1-3 Find the GCF of the set of numbers using the listing method. 1.) 18 and 272.) 32 and 72 3.) 21, 42, and 56

25. 4-2 Greatest Common Factor Example 2: Finding the GCF Find the GCF of the set of numbers. 18, 30, and 24 Method 2: Use the prime factorization. 183024

26. 4-2 Greatest Common Factor 2 5 3 2 2 3 2 3 2 3 The GCF of 18, 30, and 24 is 6. 23 =6 18 = 30 = 24 =

27. 1-2 Divide Multi-Digit Whole Numbers 1.) What is the prime factorization of each number? 2.) What are the common prime factors of ALL the numbers? 3.) Did I multiply to get my GCF?

28. 4-2 Greatest Common Factor Let’s do this one together … Find the GCF of the set of numbers using the prime factorization method. 10, 20, and 30 The GCF of 10, 20, and 30 is 10. 1.) What is the prime factorization of each number? 2.) What are the common prime factors of each number? 3.) Did I multiply to get my GCF?

29. 4-2 Greatest Common Factor TOYO using prime factorization… Find the GCF of the set of numbers. 40, 16, and 24 The GCF of 40, 16, and 24 is 8.

30. 4-2 Greatest Common Factor Exit Ticket 1. 18 and 30 2. 8, 28, 52 3. 44, 66, 88 Find the greatest common factor of each set of numbers. (Use any method)

31. 4-2 Greatest Common Factor Do Now Find the greatest common factor of each set of numbers. You must use the prime factorization method. 1.) 24, 36, and 96

32. 4-2 Greatest Common Factor Homework – Pg. 153, #’s 8-18 Even Find the greatest common factor of each set of numbers. 8.) 10 and 3510.) 36 and 7212.) 16, 40, and 8814.) 30, 45, and 7516.) 16, 48, and 72 18.) Ms. Kline makes balloon arrangements. She has 32 blue balloons, 24 yellow balloons, and 16 white balloons. Each arrangement must have the same number of each color. What is the greatest number of arrangements that Ms. Kline can make if every balloon is used?