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Today we will be learning about Prime Factorization. Warm-Up: 1.) 3 x 5 x 7 = 105

GOOD AFTERNOON!. Today we will be learning about Prime Factorization. Warm-Up: 1.) 3 x 5 x 7 = 105 2.) 2 x 2 x 2 x 3 = 24 3.) 2 x 3 x 3 x 5 = 90 4.) 7 x 7 x 11 = 539. Remember that when two or more numbers are multiplied, each number is called a FACTOR of the product*.

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Today we will be learning about Prime Factorization. Warm-Up: 1.) 3 x 5 x 7 = 105

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  1. GOOD AFTERNOON! Today we will be learning about Prime Factorization. Warm-Up: 1.) 3 x 5 x 7 = 105 2.) 2 x 2 x 2 x 3 = 24 3.) 2 x 3 x 3 x 5 = 90 4.) 7 x 7 x 11 = 539 CONFIDENTIAL

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

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

  4. Today we're going to learn how to identify COMPOSITE NUMBERS and PRIME NUMBERS COMPOSITE NUMBER - A number greater than 1 with more than two factors Can you think of a number that we would classify as COMPOSITE? Example: 28 What are its factors? The factors of 28 are 1 and 28, 2 and 14, and 4 and 7. since 28 has more than two factors, it is a composite number. CONFIDENTIAL

  5. 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? Example: 11 The factors of 11 are 1 and 11. Since there are exactly two factors, 1 and the number itself, 11 is a prime number. CONFIDENTIAL

  6. Let's try to name the first 8 prime numbers. (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 2 3 5 7 11 13 17 19 CONFIDENTIAL

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

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

  9. A factor tree can be used to find the PRIME FACTORIZATION of a number. Write the number being factored at the top. 54 54 Choose any pair of whole number factors. x 2 x 18 27 3 Continue to factor any number that is not prime. x x 9 3 2 x 9 x 3 2 Except for the order, the prime factors are the same. 3 x x 3 x 3 x 2 3 x 2 3 x 3 THE PRIME FACTORIZATION OF 54 IS 2 x 3 x 3 x 3; This can be written as 2 x 33 CONFIDENTIAL

  10. Your Turn! A factor tree can be used to find the PRIME FACTORIZATION of a number. (a) (b) 36 Write the number being factored at the top. 60 Choose any pair of whole number factors. x x 2 2 18 30 Continue to factor any number that is not prime. x x 9 15 x x 2 2 2 2 Except for the order, the prime factors are the same. 3 5 x x x 3 x 3 x x 2 2 2 2 THE PRIME FACTORIZATION OF 36 IS 2 x 2 x 3 x 3; This can be written as 22 x 32 THE PRIME FACTORIZATION OF 60 IS 2 x 2 x 3 x 5; This can be written as 22 x 3 x 5 We write the Prime Factorization in order starting with the smallest prime number. CONFIDENTIAL

  11. Here are a few more you can try! (a) (b) Write the number being factored at the top. 75 42 Choose any pair of whole number factors. x 3 25 x 2 21 Continue to factor any number that is not prime. x 5 x 5 3 x 7 x 3 2 Except for the order, the prime factors are the same. THE PRIME FACTORIZATION OF 75 IS 3 x 5 x 5; This can be written as 3 x 52 THE PRIME FACTORIZATION OF 42 IS 2 x 3 x 7 CONFIDENTIAL

  12. Let us Practice now! 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. Answer: $10 and 3 bags; $3 and 10 bags; $2 and 15 bags CONFIDENTIAL

  13. length To find the volume of a box, you can multiply its length by its height by its width. length x height x width height width The measure of the volume of a box is 357. Find its possible dimensions. Answer: 3 x 7 x 17 CONFIDENTIAL

  14. 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? Answer: 7 + 23 +29 CONFIDENTIAL

  15. 1.) What is a Prime Number? Can you give me some examples? A whole number that has exactly two unique factors, 1 and the number itself, is a prime number. Examples: 3, 5, 7, 11 2.) What is a Composite Number? Can you give me some examples? A number greater than 1 with more than two factors, is a composite number. Examples: 6, 9, 12, 15 3.) Tell whether each number is Prime, Composite, or Neither. a. 10 b. 3 c. 1 d. 61 Composite Prime Neither Prime 4.) Write the number 38 as the product of prime numbers. 38 = 2 x 19 90 5.) Use a factor tree to find the Prime Factorization of 90. The Prime Factorization of 90 is 2 x 32 x5 x 2 45 x 2 x 3 15 CONFIDENTIAL x 3 2 x x 3 5

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

  17. We also learned how to find the PRIME FACTORIZATION of a number using a Factor Tree. 56 x 2 28 x 2 x 2 14 x x 2 2 x 7 2 The Prime Factorization of 56 is 2 x 2 x 2 x 7 CONFIDENTIAL

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