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9-1 Factors & GCF

9-1 Factors & GCF. Prime Number. A number whose only factors are 1 and itself. For example: 2 (only factors are 1 * 2) 3 (only factors are 1 * 3). Composite Number. A number that has more than 2 factors. For example: 6 ( 1 * 6 and 2 * 3 ) 12 ( 1 * 12 , 3 * 4 , and 2 * 6 ).

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9-1 Factors & GCF

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  1. 9-1 Factors & GCF

  2. Prime Number • A number whose only factors are 1 and itself. For example: 2 (only factors are 1 * 2) 3 (only factors are 1 * 3)

  3. Composite Number • A number that has more than 2 factors. For example: 6 ( 1 * 6 and 2 * 3 ) 12 ( 1 * 12 , 3 * 4 , and 2 * 6 )

  4. Prime Factorization • A whole number expressed as the product of its prime factors. (Factor Tree) Example: 90 (always start with the smallest prime number)

  5. Prime Factorization • A whole number expressed as the product of its prime factors. (Factor Tree) Example: 90 / \ (always start with the 2 45 smallest prime number)

  6. Prime Factorization • A whole number expressed as the product of its prime factors. (Factor Tree) Example: 90 / \ (always start with the 2 45 smallest prime number) / \ 3 15

  7. Prime Factorization • A whole number expressed as the product of its prime factors. (Factor Tree) Example: 90 / \ (always start with the 2 45 smallest prime number) / \ 3 15 / \ 3 5

  8. Prime Factorization • A whole number expressed as the product of its prime factors. (Factor Tree) Example: 90 / \ (always start with the 2 45 smallest prime number) / \ 3 15 / \ 3 5 So, 90 = 2*3*3*5 or 90 = 2*32*5

  9. A monomial is in completely factored form when: • It is expressed as a product of prime numbers • No exponents are greater than 1

  10. 1. Factor the number (tree)2. Write out the variables 12a2b2

  11. 1. Factor the number (tree)2. Write out the variables 12 a2b2 / \ 2 6 / \ 2 3

  12. 1. Factor the number (tree)2. Write out the variables 12 a2b2 / \ 2 6 / \ 2 3 So, 12a2b2= 2 * 2 * 3 * a * a * b * b

  13. *Negative integers…Always start the tree with -1, then continue pulling out prime factors -66pq2 / \ -1 66

  14. *Negative integers…Always start the tree with -1, then continue pulling out prime factors -66pq2 / \ -1 66 / \ 2 33 / \ 3 11

  15. *Negative integers…Always start the tree with -1, then continue pulling out prime factors -66pq2 / \ -1 66 / \ 2 33 / \ 3 11 So, -66pq2= -1*2*3*11*p*q*q

  16. Find the GCF 48 and 60

  17. Find the GCF (1. factor tree) 48 and 60 / \ / \ 2 24 2 30

  18. Find the GCF (1. Factor tree ) 48 and 60 / \ / \ 2 24 2 30 / \ / \ 2 12 2 15

  19. Find the GCF (1. Factor tree ) 48 and 60 / \ / \ 2 24 2 30 / \ / \ 2 12 2 15 / \ / \ 2 6 3 5

  20. Find the GCF (1. Factor tree ) 48 and 60 / \ / \ 2 24 2 30 / \ / \ 2 12 2 15 / \ / \ 2 6 3 5 / \ 2 3

  21. Find the GCF (1. Factor tree, 2. Look for pairs ) 48 and 60 / \ / \ 2 24 2 30 / \ / \ 2 12 2 15 / \ / \ 2 6 3 5 / \ 2 3 48 = 2 * 2 * 2 * 2 * 3 60 = 2 * 2 * 3 * 5

  22. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) 48 and 60 / \ / \ 2 24 2 30 / \ / \ 2 12 2 15 / \ / \ 2 6 3 5 / \ 2 3 GCF = 2*2*3 = 12 48 = 2 * 2 * 2 * 2 * 3 60 = 2 * 2 * 3 * 5

  23. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) What about 15 and 16?

  24. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) What about 15 and 16? 15 16 / \ / \ 3 5 2 8 /\ 2 4 /\ 2 2

  25. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) 16 = 2 * 2 * 2 * 2 15 = 3 * 5 There are NO pairs. These numbers have nothing in common and are therefore relatively prime. They do not have a GCF.

  26. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) Try: 36x2y and 54xy2z

  27. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) 36x2y and 54xy2z / \ / \ 2 18 2 27 / \ / \ 2 9 3 9 /\ /\ 3 3 3 3

  28. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) 36x2y and 54xy2z / \ / \ 2 18 2 27 / \ / \ 2 9 3 9 /\ /\ 3 3 3 3 36x2y = 2 * 2 * 3 * 3 * x * x * y 54xy2z=2 * 3 * 3 * 3 * x * y * y * z

  29. Find the GCF(1. Factor tree, 2. Look for pairs, 3. Multiply common factors for GCF) 36x2y = 2 * 2 * 3 * 3 * x * x * y 54xy2z=2 * 3 * 3 * 3 * x * y * y * z GCF = 2 * 3 * 3 * x * y = 18xy

  30. Your turn to try some now! Find the GCF • 18xy , 36y2 • 15r2 , 35s2 , 70r5 • 12a2b , 90a2b2c • 25n , 21m

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