VIEWS: 460 PAGES: 36 CATEGORY: Education POSTED ON: 4/7/2010 Public Domain
Divisibility Rules & Prime Factorization Lesson 4-2 The standard you are working on Number Sense 1.4 (grade 5) Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor You will be building upon this standard so that you can successfully work toward the understanding of sixth grade standard, Number Sense 2.4 The standard you are working toward Number Sense 2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). This lesson will be broken into three parts Prime vs. composite numbers Divisibility rules Prime factorization Using divisibility rules to find prime factors Using factor trees to find the prime factorization of numbers Putting prime factors into exponential form as needed Prime Numbers vs. Composite Numbers Key Vocabulary Factor Prime number Composite number Factor The numbers that are multiplied to give a product 15 = 3 x 5 3 and 5 are factors of 15 Composite Number Any factor that has at least 3 factors including one and itself 4: 1, 2, and 4 6: 1, 2, 3, and 6 9: 1, 3, and 9 10: 1, 2, 5, 10 Prime number Any number who has only two factors: one and itself 1 is not a prime number; it is a unit Its only factor is 1 Examples of prime numbers 2, 3, 5, 7, 11 Using a 100 chart to find prime numbers between 1 and 100… Here is how… 2 is a prime number. All other multiples of 2 are composite. Cross them off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 3 is a prime number. All other multiples of 3 are composite. Cross them off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 5 is a prime number. All other multiples of 5 are composite. Cross them off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 7 is a prime number. All other multiples of 7 are composite. Cross them off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Why did we skip 6? The factors of 6 are 2 and 3. We already crossed off all factors of two and three. 11 is a prime number. All other multiples of 11 are composite. Cross them off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 13 is a prime number. All other multiples of 13 are composite. Cross them off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 17 is a prime number. All other multiples of 17 are composite. They are already crossed off. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Continue this process until all prime numbers are circled and all composite numbers are crossed off. All of the orange numbers on this chart are prime. Write them down. Refer to them so you don’t waste time trying to factor them. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 A Rhyme to Help Us Remember Prime number Prime number What do you see? I see no other factors Except for one and me. Composite number Composite number What do you see? I see at least three factors Including one and me. Divisibility Rules The Rule for 2 If a number is even, then it is divisible by two. An even number is any number that ends in a 2, 4, 6, 8, or 0 93 76 52 98 100 The Rule for 3 Add up all the digits. If the sum of all digits is divisible by 3, then the whole number is divisible by 3! 6321 = 6 + 3 + 2 + 1 =12 3 goes into 12 evenly, so 6321 is divisible by 3 63 28 981 21 762 The Rule for 4 The last two numbers are either 00 or they are divisible by 4. An even number is any number that ends in a 2, 4, 6, 8, or 0 804 217 724 916 600 The Rule for 5 The number ends in a 5 or a zero. 93 90 75 55 100 The Rule for 9 Add up all the digits. If the sum of all digits is divisible by 9, then the whole number is divisible by 9! 6327 = 6 + 3 + 2 + 7 =18 9 goes into 18 evenly, so 6327 is divisible by 9 81 312 1125 414 882 The Rule for 10 The number ends in a zero 9003 5840 6430 1020 70 Divisibility Rules Explained 1. Video from teachertube.com 2. Explanation from Mrs. Glosser Let’s Practice… Interactive Divisibility Rules Practice Prime Factorization Writing a number as a product of its primes Factor Trees A video from TeacherTube.com Interactive Practice for Factor Trees 1. Virtual Manipulatives 2. Interactive Practice 1 3. Interactive Practice from MathPlayground.com The Birthday Cake Method a.k.a. The Box Method An alternative to factor trees A video from YouTube Challenge Problem Use what you know about multiplying whole numbers by variables and exponents to make a factor tree for the following monomial 45x3 45 x3 9 5xx x 3 3 A Random Thought about Prime Numbers Brought to you from YouTube.com