1. 4-2 Factors and Prime Factorization Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 4-2 Factors and Prime Factorization Warm Up Identify each number as prime or composite. 1. 192. 82 3. 574. 85 5. 1016. 121 prime composite prime

3. 4-2 Factors and Prime Factorization Problem of the Day At the first train stop, 7 people disembarked. At the second stop, 8 people disembarked. At the fourth stop, the last 6 people disembarked. If there were 28 people on the train before the first stop, how many people left at the third stop? 7 people left at the third stop

4. 4-2 Factors and Prime Factorization Prep for MA.6.A.5.1 Use equivalent forms of fractions, decimals…to solve problems. Also Review of MA.5.A.2.4 Sunshine State Standards

5. 4-2 Factors and Prime Factorization Vocabulary factor prime factorization

6. 4-2 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.

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

8. 4-2 Factors and Prime Factorization Additional Example 1B: Finding Factors List all of the factors of the number 19. B. 19 19 = 1 19Begin listing factors in pairs. 19 is not divisible by any other whole numbers. The factors of 19 are 1 and 19.

9. 4-2 Factors and Prime Factorization Check It Out: Example 1A List all of the factors of the number 12. A. 12 12 = 1 12 12 = 2 6 1 is a factor. 2 is a factor. 3 is a factor. 4 and 3 have already been listed, so stop here. 12 = 4 3 1243126 The factors of 12 are 1, 2, 3, 4, 6, and 12 12 = 3 4 You can draw a diagram to illustrate the factor pairs. Begin listing factors in pairs.

10. 4-2 Factors and Prime Factorization Check It Out: Example 1B List all of the factors of the number 11. B. 11 11 = 1 11Begin listing factors in pairs. 11 is not divisible by any other whole numbers. The factors of 11 are 1 and 11.

11. 4-2 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. 4-2 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. 4-2 Factors and Prime Factorization Additional Example 2A: Writing Prime Factorizations 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. 4-2 Factors and Prime Factorization Additional Example 2B: Writing Prime Factorizations Method 2: Use a ladder diagram. Choose a prime factor of 45 to begin. Keep dividing by prime factors until the quotient is 1. 345 3 1 15 5 5 45 = 3 3 5 545 3 1 9 3 3 45 = 5 3 3 The prime factorization of 45 is 3 3 5 or 3 2 5. Write the prime factorization of 45.

15. 4-2 Factors and Prime Factorization In Example 2, 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.

16. 4-2 Factors and Prime Factorization Check It Out: Example 2A 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.

17. 4-2 Factors and Prime Factorization Check It Out: Example 2B Write the prime factorization of 36. Method 2: Use a ladder diagram. Choose a prime factor of 36 to begin. Keep dividing by prime factors until the quotient is 1. 336 2 1 12 6 2 36 = 3 2 2 3 The prime factorization of 36 is 3 2 2 3, or 3 2 2 3. 336 3 1 12 2 4 36 = 3 3 2 2 3 3 2 2