1. Factors and Prime Factors 5.2

2. What Will We Accomplish? After reviewing the characteristics of prime and composite numbers.... We will write the prime factorization of composite numbers. We will look at this skill in three ways. The “Think Box” method will be the most useful in future math classes.

3. Prime or Composite Review It is helpful to identify a number as prime or composite when trying to simplify a value. Prime numbers have only two factors: Itself and the number 1. The number “1” is neither prime nor composite. It has only one factor. The number 2 is the only even number that is prime.

4. Factors are multiplication “facts.” Factors: whole numbers that are multiplied together to form a product Prime factorization: writing a product using ONLY PRIME NUMBERS as a multiplication problem. 8 = 2 x 2 x 2 = 2 3

5. Prime Factorization Method 1: Factor Trees Start with the composite number, and break it into two of its factors. 48 6 X 812 X 4 2 X 34 X 2 2 X 2 000 0 0 The prime factors are 2∙2∙2∙3∙2= 2 4 ∙ 3 2 x 2 6 X 2 3 X 2 00 0 0 0

6. Prime Factorization: Factor Tree Practice Start with the composite number, and break it into two of its factors. 30 50 3 x 10 5 x 10 3 x 2 x 5 2 x 3 x 5 2 x 5 x 5 = 2 x 5 2 0 00 0 0 3 x 3 5 x 2 9 x 10 00 0 0 0 90 2 x 5 2 x 5 x 3 x 3 = 2 x 3 2 x 5

7. Remember Our Objective! We are rewriting composite numbers as prime factors. This means we are writing multiplication problems that ONLY have prime factors in them!

8. Prime Factorization: Method 2 Division Ladders When using a division ladder, use only primes to divide. 482 242 12 2 62 3 These are your prime factors: 2 x 2 x 2 x 2 x 3 303 102 5 The prime factors are 2 x 3 x 5 Add this to your notes.

9. Prime Factorization: Division Ladder Practice Remember, use only primes to divide. 1002 502 25 5 5 2 x 2 x 5 x 5 = 2 2 x 5 2 2505 505 10 5 x 5 x 5 x 2 = 2 x 5 3 5 2

10. Prime Factorization: Method 3 Think Box Primes This is a new method. This is the method that will help you with the rest of the chapter and into next year. It is shown in a different form in your text. 48 = Make a “think box” to organize your thoughts. List two factors that = 48. 6 x 8 = Take one factor at a time and break it into prime factors. 3 x 2 Remembering that 8 = 2 x 2 x 2 will save you a tremendous amount of time! x 2 x 2 x 2 90 =9 x 10 =3 x 2 x 5 2 x 3 2 x 5

11. 120 =12 x 10 =2 x 2 x 3 x 2 x 52 3 x 3 x 5 66 =6 x 11 =2 x 3 x 11 88 = Remember the 8!!!! 8 x 11 =2 x 2 x 2 x 11 2 3 x 11= Think Box Practice 36 =6 x 6 =2 x 3 x 2 x 3 2 2 x 3 2 45 =5 x 9 =5 x 3 x 35 x 3 2 1500 =15 x 100 =3 x 53 x 2 2 x 5 3 2 x 5 x 2 x 5 x 2 x 5 x 2 x 5

12. Have We Met Our Objective? Did we write composite numbers in the form of prime factorizations? Did you find one method you preferred over the others? Remember, you do not always have to use one method. You can use a method that works best for a specific problem. However….which one will be the most help in future math classes?

13. Think in terms of primes. Speed limits? 7 x 2 x 5 Ages? 2 x 2 x 3 Grades? 2 x 5 x 2 x 5 PRIMES