1. CONFIDENTIAL1 Today we will be learning about Prime Factorization. Warm-Up: 1.)3 x 5 x 7 = 2.)2 x 2 x 2 x 3 = 3.)2 x 3 x 3 x 5 = 4.)7 x 7 x 11 = GOOD AFTERNOON!

2. CONFIDENTIAL2 Remember that when two or more numbers are multiplied, each number is called a FACTOR of the product*. 1 x 6 = 6and2 x 3 = 6 1 & 6, and 2 & 3 are the factors of 6 * Remember that "product" is the answer to a multiplication problem.

3. CONFIDENTIAL3 1234681224 We also learned how to find all the factors of a number by RAINBOW FACTORING The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24

4. CONFIDENTIAL4 COMPOSITE NUMBER - A number greater than 1 with more than two factors Today we're going to learn how to identify COMPOSITE NUMBERS and PRIME NUMBERS Can you think of a number that we would classify as COMPOSITE? What are its factors?

5. CONFIDENTIAL5 PRIME NUMBERS A Prime Number is a whole number that has exactly two factors..... 1 and itself Can you think of a number like that?

6. CONFIDENTIAL6 Let's try to name the first 8 prime numbers. 235711131719 (Hint: The numbers 0 and 1 are neither prime nor composite. 1 has only 1 factor. 0 has an infinite number of factors. To Check

7. CONFIDENTIAL7 Tell me whether each number below is Prime Composite Neither (a) 28 (b) 11 (c) 48 (d) 7 (e) 81 (f) 1

8. CONFIDENTIAL8 Did you know that EVERY Composite Number can be expressed as a product of prime numbers??? This is called PRIME FACTORIZATION.

9. CONFIDENTIAL9 A factor tree can be used to find the PRIME FACTORIZATION of a number. Write the number being factored at the top. Choose any pair of whole number factors. Continue to factor any number that is not prime. Except for the order, the prime factors are the same. 54 3 18 3 2 9 3 2 3 3 x x x 2 27 2 3 9 2 3 3 3 x x x x x x x x x THE PRIME FACTORIZATION OF 54 IS 2 x 3 x 3 x 3; This can be written as 2 x 3 3

10. CONFIDENTIAL10 A factor tree can be used to find the PRIME FACTORIZATION of a number. Your Turn! 36 60 We write the Prime Factorization in order starting with the smallest prime number. Write the number being factored at the top. Choose any pair of whole number factors. Continue to factor any number that is not prime. Except for the order, the prime factors are the same. (a) (b)

11. CONFIDENTIAL11 75 42 Here are a few more you can try! Write the number being factored at the top. Choose any pair of whole number factors. Continue to factor any number that is not prime. Except for the order, the prime factors are the same. (a)(b)

12. CONFIDENTIAL12 Very Good Job! Let's take a short break!

13. CONFIDENTIAL13 Puzzle Can you move just one match to leave a square? Solution: 4 is a square! It's the square of 2.

14. CONFIDENTIAL14 Jessica bought bags of snacks at the store and each bag cost the same price. She spent a total of $30. Find three possible costs per bag and the number of bags she could have purchased. Let us Practice now!

15. CONFIDENTIAL15 length height width To find the volume of a box, you can multiply its length by its height by its width. length x height x width The measure of the volume of a box is 357. Find its possible dimensions.

16. CONFIDENTIAL16 Did you know that all odd numbers greater than 7 can be expressed as the sum of 3 Prime Numbers??? Which three prime numbers have a sum of 59?

17. CONFIDENTIAL17 1.) What is a Prime Number? Can you give me some examples? 3.) Tell whether each number is Prime, Composite, or Neither. a.10 b.3 c.1 d. 61 4.) Write the number 38 as the product of prime numbers. 5.) Use a factor tree to find the Prime Factorization of 90. 2.) What is a Composite Number? Can you give me some examples?

18. CONFIDENTIAL18 You worked very hard today! Prime Number Composite Number Neither Prime nor Composite A whole number that has exactly 2 factors - 1 and itself. A number greater than 1 with more than 2 factors. "1" has only 1 factor "0" has an infinite number of factors. Let's review what we learned. Examples: 3, 7, 19 Examples: 4, 12, 22 Examples: 1 and 0

19. CONFIDENTIAL19 We also learned how to find the PRIME FACTORIZATION of a number using a Factor Tree. 56 2 28 2142 2 72 2 x x x x x x The Prime Factorization of 56 is 2 x 2 x 2 x 7