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Lesson 3 Contents Objective Find the prime factorization of a composite number

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Lesson 3 Contents Vocabulary Factor Two or more numbers that are multiplied 3 4 both 3 and 4 are factors

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Lesson 3 Contents Vocabulary Prime number A whole number that has exactly 2 unique factors, 1 and the number itself 2Factors 1 & 2 3Factors 1 & 3 5Factors 1 & 5 13Factors 1 & 13 Most Common Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47

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Lesson 3 Contents Vocabulary Composite number A number greater than 1 with more than 2 factors 4Factors 1, 2, & 4 12Factors 1, 2, 3, 4, 6, & 12

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Lesson 3 Contents Vocabulary Prime factorization Expressing a composite number as a product of prime 12 = 2 2 3 54 = 2 3 3

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Lesson 3 Contents Example 1Identify Prime and Composite Numbers Example 2Identify Prime and Composite Numbers Example 3Find Prime Factorization

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Example 3-1a Tell whether 13 is prime, composite, or neither. Answer: prime The factors of 13:1 and 13 1/3 Has 2 factors which are 1 and the number itself Fits the definition of “prime” number

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Example 3-1b Tell whether 35 is prime, composite, or neither. 1/3 Answer: composite

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Example 3-2a Tell whether the number 20 is prime, composite, or neither. Answer: composite The factors of 20:1 and 20, 2 and 10, 4 and 5 2/3 Fits the definition of “composite” number 20 has more than 2 factors

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Example 3-2b Tell whether the number 41 is prime, composite, or neither. 2/3 Answer: prime

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Example 3-3a Find the prime factorization of 96. 3/3 96 Write the number Draw prime factorization brackets Decide on prime number that will go evenly into 96 Think about divisibility rules Note: If even consider 2 If ones digits is 0 or 5 consider 5

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Example 3-3a Find the prime factorization of 96. 3/3 96 The one’s digit is 6 which is divisible by 2 Place the prime number 2 to the left of the bracket Divide 96 by 2 and place the answer below the bracket 2 48 Determine if 48 is a prime number

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Example 3-3a Find the prime factorization of 96. 3/3 96 48 is not prime so place another prime factorization bracket under 48 2 48 Since 48 is divisible by 2, place the 2 to the left of the bracket Divide 48 by 2 and place the answer below the bracket Determine if 24 is a prime number 2 The one’s digit is 8 which is divisible by 2 24

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Example 3-3a Find the prime factorization of 96. 3/3 96 The one’s digit is 4 so 24 is divisible by 2 2 48 2 24 24 is not prime so place another prime factorization bracket under 24 Since 24 is divisible by 2, place the 2 to the left of the bracket 2 Divide 24 by 2 and place the answer below the bracket 12 Determine if 12 is a prime number

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Example 3-3a Find the prime factorization of 96. 3/3 96 The one’s digit is 2 so 12 is divisible by 2 2 48 2 24 12 is not prime so place another prime factorization bracket under 12 Since 12 is divisible by 2, place the 2 to the left of the bracket 2 Divide 12 by 2 and place the answer below the bracket 12 Determine if 6 is a prime number 2 6

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Example 3-3a Find the prime factorization of 96. 3/3 96 The one’s digit is 6 so 6 is divisible by 2 2 48 2 24 6 is not prime so place another prime factorization bracket under 6 Since 6 is divisible by 2, place the 2 to the left of the bracket 2 Divide 6 by 2 and place the answer below the bracket 12 Determine if 3 is a prime number 2 6 2 3

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Example 3-3a Find the prime factorization of 96. 3/3 96 The factors of 3 are 1 and 3 2 48 2 24 3 fits the definition of a prime number 2 122 6 2 3 Finished prime factoring so now write answer

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Example 3-3a Find the prime factorization of 96. 3/3 96 Write the smallest prime number which in this case is 2 2 48 2 24 Circle all the 2’s that were used in prime factoring, counting as you go 2 122 6 2 3 Since there were 5 two’s, place an exponent of 5 with the 2 in your answer 2 5

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Example 3-3a Find the prime factorization of 96. 3/3 96 Next put a multiplication sign 2 48 2 24 2 122 6 2 3 2 5 Note: Do not use “x” for multiplication Circle all the 3’s that were used in prime factoring, counting as you go Write the next smallest prime number which in this case is 3 3

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Example 3-3a Find the prime factorization of 96. 3/3 96 Since there is only 1 three, do not put an exponent 2 48 2 24 2 122 6 2 3 2 5 You are finished after you circle your answer! Yippee 3 Answer: Note: Any prime number can be used. If you start with an odd number, you will not start with 2

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Example 3-3b Find the prime factorization of 72. * 3/3 Answer: 2 3 3 2

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End of Lesson 3 Lesson 1:3Prime Factors14 - 46 Even Assignment

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