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Prime Factorization of Composite Numbers

Learn how to find the prime factorization of composite numbers in this lesson. Identify prime and composite numbers, and practice finding the factors and prime factorization.

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Prime Factorization of Composite Numbers

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  1. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

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

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

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

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

  7. Lesson 3 Contents Vocabulary Prime factorization Expressing a composite number as a product of prime 12 = 22 3 54 = 2  33

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

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

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

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

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

  13. Example 3-3a Find the prime factorization of 96. Write the number 96 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 3/3

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

  15. Example 3-3a Find the prime factorization of 96. The one’s digit is 8 which is divisible by 2 2 96 48 is not prime so place another prime factorization bracket under 48 2 48 24 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 3/3

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

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

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

  19. Example 3-3a Find the prime factorization of 96. The factors of 3 are 1 and 3 2 96 3 fits the definition of a prime number 2 48 24 2 Finished prime factoring so now write answer 2 12 2 6 3 3/3

  20. Example 3-3a Find the prime factorization of 96. Write the smallest prime number which in this case is 2 2 96 Circle all the 2’s that were used in prime factoring, counting as you go 2 48 24 2 Since there were 5 two’s , place an exponent of 5 with the 2 in your answer 2 12 2 6 3 5 2 3/3

  21. Example 3-3a Find the prime factorization of 96. Next put a multiplication sign Note: Do not use “x” for multiplication 2 96 2 48 Write the next smallest prime number which in this case is 3 24 2 2 12 Circle all the 3’s that were used in prime factoring, counting as you go 2 6 3 5 2  3 3/3

  22. Example 3-3a Find the prime factorization of 96. Since there is only 1 three , do not put an exponent 2 96 2 48 You are finished after you circle your answer! Yippee 24 2 2 12 Note: Any prime number can be used. If you start with an odd number, you will not start with 2 2 6 3 5 2  Answer: 3 3/3

  23. Example 3-3b * Find the prime factorization of 72. Answer: 23 32 3/3

  24. End of Lesson 3 Assignment

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