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Classifying Numbers as Prime or Composite

Learn about prime and composite numbers, factorization, and finding the greatest common factor (GCF) through examples and practice exercises.

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Classifying Numbers as Prime or Composite

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  1. Lesson 1 Contents Example 1 Classify Numbers as Prime or Composite

  2. Definitions Factor - One of two numbers multiplied to obtain a product. 2 x 3 = 6 thus, 2 & 3 are factors of 6 Prime Number - A whole number, greater than 1, whose only factors are 1 and itself. The only even prime number is 2. Composite Number - A whole number, greater than 1, that has more than two factors.

  3. Example 1-1a Factor 22. Then classify it as prime or composite. To find the factors of 22, list all pairs of whole numbers whose product is 22. Answer: Since 22 has more than two factors, it is a compositenumber. The factors of 22, in increasing order, are 1, 2, 11, and 22.

  4. Example 1-1a Factor 31. Then classify it as prime or composite. The only wholenumbers that can be multiplied together to get 31 are 1 and 31. Answer: The factors of 31 are 1 and 31.Since the only factors of 31 are 1 and itself, 31 is a prime number.

  5. Example 1-1b Factor each number. Then classify it as primeor composite. a. 17 b. 25 Answer: 1, 17; prime Answer: 1, 5, 25; composite

  6. Example 2 Prime Factorization of a Positive Integer

  7. 21 4 3 7 2 2 and Answer: Thus, the prime factorization of 84 is or Example 1-2a Find the prime factorization of 84. Use a factor tree. 84 All of the factors in the last branch of the factor tree are prime.

  8. 15 4 60 = 15 * 4 3 5 2 2 and 15 = 3 * 5 Answer: Thus, the prime factorization of 60 is or 2*2*3*5 22*3*5 Example 1-2b Find the prime factorization of 60. 60 All of the factors in the last branch of the factor tree are prime.

  9. Example 3 Prime Factorization of a Negative Integer

  10. Definitions Prime Factorization - When a whole number is expressed as the product of factors that are all prime numbers.

  11. Answer: The prime factorization of –132 is or Example 1-3a Find the prime factorization of –132. -132 -1 132 4 33 2 2 3 11

  12. Answer: Example 1-3b Find the prime factorization of –154.

  13. Example 4 Prime Factorization of a Monomial

  14. Definition Prime factorization of a constant (just a number) can have exponents greater than 1, but prime factorization of variable values canNOT!

  15. Factor completely. Answer: in factored form is Example 1-4a 18 x3 y3 2 9 x x x y y y 3 3 This can also be written as 2*32*x*x*x*y*y*y

  16. Factor completely. Answer: in factored form is-1*2*13*r*s*t*t Example 1-4a -26 r s t2 -1 26 t t 2 13

  17. Factor each monomial completely. a. b. Answer: Answer: Example 1-4b

  18. Example 5 GCF of a Set of Monomials

  19. Definitions Greatest Common Factor (GCF)- The product of the prime factors that are common to two or more integers.

  20. Factor each number. The integers 12 and 18 have one 2 and one 3 as common prime factors. The product of thesecommon prime factors, or 6, is the GCF. Example 1-5a Find the GCF of 12 and 18. Circle the common prime factors. Answer: The GCF of 12 and 18 is 6.

  21. Find the GCF of . Factor each number. Answer: The GCF of and is . Example 1-5a Circle the common prime factors.

  22. Find the GCF of each set of monomials. a. 15 and 35 b. and Answer: Example 1-5b Answer: 5

  23. Example 6 Use Factors

  24. CraftsRene has crocheted 32 squares for an afghan. Each square is 1 foot square. She is not sure how she will arrange the squares but does know it will be rectangular and have a ribbon trim. What is the maximum amount of ribbon she might need to finish an afghan? Find the factors of 32 and draw rectangles with each length and width. Then find each perimeter. The factors of 32 are 1, 2, 4, 8, 16, 32.

  25. Example 1-6a The greatest perimeter is 66 feet. The afghan with this perimeter has a length of 32 feet and a width of 1 foot. Answer: The maximum amount of ribbon Rene will need is 66 feet.

  26. Example 1-6b Mary wants to plant a rectangular flower bed in her front yard with a stone border. The area of the flower bed will be 45 square feet and the stones are one foot square each. What is the maximum number of stones that Mary will need to go around all four sides of the flower bed? Find the factors of 45 and draw rectangles with each length and width. Then find each perimeter. The factors of 45 are 1, 3, 5, 9, 15, 45.

  27. Example 1-6c The greatest perimeter is 92 feet. The flower bed with this perimeter has a length of 45 feet and a width of 1 foot. Answer: The maximum amount of stones Mary will need is 92 feet.

  28. Thank you for participating in today’s lesson.Here is your reward: Homework: Pages 477-478 20-60 even

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