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