1. 5 Minute Check Find the prime factors for the following. Complete on the back of your homework. 1. 42 2. 10 3. 40 4. 51

2. 5 Minute Check Find the prime factors for the following. Complete on your homework. 1. 42

3. 5 Minute Check Find the prime factors for the following. Complete on your homework. 1.42 42 / \ 2 21 I / \ 2 x 3 x 7

4. 5 Minute Check Find the prime factors for the following. Complete on your homework. 2. 10

5. 5 Minute Check Find the prime factors for the following. Complete on your homework. 2. 10 10 / \ 2 x 5

6. 5 Minute Check Find the prime factors for the following. Complete on your homework. 3. 40

7. 5 Minute Check Find the prime factors for the following. Complete on your homework. 3. 40 40 / \ 2 20 I / \ 2 x 2 x 10 I I / \ 2 x 2 x 2 x 5

8. 5 Minute Check Find the prime factors for the following. Complete on your homework. 4. 51

9. 5 Minute Check Find the prime factors for the following. Complete on your homework. 4. 51 51 / \ 3 17

10. Flashcards

11. Thursday, Aug 27 Lesson 1.1 Factors and Multiples

12. Objective: To find the Greatest Common Factor and the Least Common Multiple.

13. Factors and Multiples A common factor is a number that is a factor of two or more numbers.

14. Factors and Multiples A common factor is a number that is a factor of two or more numbers. The greatest of the common factor of two or more numbers is called the greatest common factor (GCF).

15. Factors and Multiples Greatest Common Factor would be the largest number that is in all factor rainbows of two or more numbers.

16. Factors and Multiples There are two ways to find the GCF -Factor List (Factor Rainbows) -Factor Trees

17. Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – Make a factor rainbow for each number. (Hint: The first factor in a factor rainbow will always be a 1)

18. Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – Make a factor rainbow for each number. 8: ?

19. Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – Make a factor rainbow for each number. 8:1, 2, 4, 8 12: ?

20. Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – Make a factor rainbow for each number. 8:1, 2, 4, 8 12:1,2,3,4,6,12

21. Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 2 – Circle the greatest number that is in all lists. 8:1, 2, 4, 8 12:1,2,3,4,6,12

22. Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 2 – Circle the greatest number that is in all lists. 8:1, 2, 4, 8 12:1,2,3,4,6,12 The GCF of 8 and 12 is 4.

23. Factors and Multiples What is the GCF of 20 and 32? Step 1 – ?

24. Factors and Multiples What is the GCF of 20 and 32? 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 Step 2 – ?

25. Factors and Multiples What is the GCF of 20 and 32? 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 The GCF of 20 and 32 is 4.

26. Factors and Multiples What is the GCF of 24 and 30? Do this on your own.

27. Factors and Multiples What is the GCF of 24 and 30? 24: 1, 2, 3, 4, 6, 8, 12, 24 30, 1, 2, 3, 5, 6, 10, 15, 30 The GCF of 24 and 30 is 6.

28. Factors and Multiples We can also find the GCF with factor trees.

29. Factors and Multiples What is the GCF of 8 and 12? Factor Tree Method Step 1 – Create a factor tree for each number.

30. Factors and Multiples What is the GCF of 8 and 12? Factor Tree Method Step 1 – Create a factor tree for each number. 812 / \ / \ 2 x 4 2 x 6 I / \ I / \ 2 x 2 x 2 2 x 2 x 3 Write this down

31. Factors and Multiples What is the GCF of 8 and 12? Factor Tree Method Step 2 – Multiply the common prime factors. 812 / \ / \ 2 x 4 2 x 6 I / \ I / \ 2 x 2 x 2 2 x 2 x 3

32. Factors and Multiples What is the GCF of 8 and 12? Factor Tree Method Step 2 – Multiply the common prime factors. 812 / \ / \ 2 x 4 2 x 6 I / \ I / \ 2 x 2 x 2 2 x 2 x 3 The GCF is 2 x 2, or 4

33. Factors and Multiples Generally the factor tree method is best when the numbers are larger.

34. Factors and Multiples What is the GCF of 15 and 30?

35. Factors and Multiples For example, what is the GCF of 15 and 30? Since 15 goes into 30 with no remainder, 15 is the GCF. We can prove this with factor lists……..

36. Factors and Multiples For example, what is the GCF of 15 and 30? 15: 1, 3, 5, 15 30: 1, 2, 3, 5, 6, 10, 15, 30

37. Factors and Multiples Mr. Avery’s GCF Rule – If the smaller number goes into the larger number(s), the smaller number is the GCF.

38. Factors and Multiples What is the GCF of 18 and 30. Do this on your own.

39. Factors and Multiples What is the GCF of 18 and 30. 18; 1, 2, 3, 6, 9, 18 30; 1, 2, 3, 5, 6, 10, 15, 30 The GCF of 18 and 30 is 6.

40. Factors and Multiples What is the GCF of 6 and 12? Do this on your own.

41. Factors and Multiples What is the GCF of 6 and 12? Mr. Avery’s Rule - Since 6 x 2 = 12 6 is the GCF. You can prove this by factor lists. 6; 1, 2,3, 6 12; 1, 2, 3, 4, 6, 12

42. Factors and Multiples What is the GCF of any two prime numbers?

43. Factors and Multiples What is the GCF of any two prime numbers? Since prime numbers have a factor list of 1 and itself, the GCF would be 1. Example – 43; 1, 43 31; 1, 31

44. Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? Do this on your own.

45. Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? 49: 1, 7, 49 42: 1, 2, 6, 7, 21, 42 21: 1, 3, 7, 21 The most she could have charged for each bracelet was $7.

46. Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? If she sold them for $7, how many did she sell on Friday?

47. Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? If she sold them for $7, how many did she sell on Friday? $49 ÷ $7 = 7 bracelets

48. Factors and Multiples The least number that is a multiple of two or more whole numbers is the least common multiple (LCM) of the numbers.

49. Factors and Multiples Least Common Multiple would be the smallest number that is in all multiple lists.

50. Factors and Multiples Find the LCM of 2 and 3. Find the LCM Step 1 – Make a multiples list (skip counting) for each number. What is the multiples list of 2?

51. Factors and Multiples Find the LCM of 2 and 3. Find the LCM Step 1 – Make a multiples list (skip counting) for each number. 2; 2, 4, 6, 8, 10….. What is the multiples list of 3?

52. Factors and Multiples Find the LCM of 2 and 3. Find the LCM Step 1 – Make a multiples list (skip counting) for each number. 2; 2, 4, 6, 8, 10….. 3; 3, 6, 9, 12, 15…..

53. Factors and Multiples Find the LCM of 2 and 3. Find the LCM Step 2 – Circle the smallest number that is in all lists. 2; 2, 4, 6, 8, 10….. 3; 3, 6, 9, 12, 15…..

54. Factors and Multiples Find the LCM of 2 and 3. Find the LCM Step 2 – Circle the smallest number that is in all lists. 2; 2, 4, 6, 8, 10….. 3; 3, 6, 9, 12, 15….. The LCM of 2 and 3 is 6.

55. Factors and Multiples Find the LCM of 2 and 6. Step 1 ?

56. Factors and Multiples Find the LCM of 2 and 6. 2; 2, 4, 6, 8, 10….. 6; 6, 12, 18, 24….. Step 2?

57. Factors and Multiples Find the LCM of 2 and 6. 2; 2, 4, 6, 8, 10….. 6; 6, 12, 18, 24….. The LCM of 2 and 6 is 6.

58. Factors and Multiples Mr. Avery’s LCM Rule – If the smaller number goes into the larger number(s), the larger number is the LCM. Since 2 x 3 = 6, the LCM of 2 and 6 is 6..

59. Factors and Multiples Find the LCM of 6 and 10. Do this on your own.

60. Factors and Multiples Find the LCM of 6 and 10. 6: 6, 12, 18, 24, 30, 36, 42, 48…… 10: 10, 20, 30, 40, 50, 60,…….. The LCM of 6 and 10 is 30.

61. Factors and Multiples Find the LCM of 4, 5 and 10. Do this on your own.

62. Factors and Multiples Find the LCM of 4, 5 and 10. 4; 4, 8, 12, 16, 20, 24…. 5; 5, 10, 15, 20, 25….. 10; 10, 20, 30 …… The LCM of 4, 5, and 10 is 20.

63. Factors and Multiples Find the LCM of 14 and 21. Do this on your own.

64. Factors and Multiples Find the LCM of 14 and 21. 14: 14, 28, 42, 56, 70….. 21: 21, 42, 63, 84…… The LCM of 14 and 21 is 42.

65. Factors and Multiples Find the LCM of 7 and 9. Do this on your own

66. Factors and Multiples Find the LCM of 7 and 9. 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77….. 9: 9, 18, 27, 36, 45, 54, 63, 72, 81……… The LCM of 7 and 9 is 63.

67. Factors and Multiples Find the LCM of 3, 5 and 7. Do this on your own

68. Factors and Multiples Find the LCM of 3, 5 and 7. 3; 3, 6, 9, 12, 15, 18,21, 24, 27, 30, 33, 36, ….. 5; 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,…… 7; 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77,……

69. Factors and Multiples Find the LCM of 3, 5 and 7. Mr. Avery’s Second LCM Rule – If all the numbers are prime, the LCM is the product of those numbers. Since 3, 5, and 7 are prime, the LCM is the product. The LCM is 105 (3 x 5 x 7)

70. Factors and Multiples Find the LCM of 9, 12 and 18. Do this on your own

71. Factors and Multiples Find the LCM of 9, 12 and 18. 9; 9, 18, 27, 36, 45, 54…… 12; 12, 24, 36, 48…… 18; 18, 36, 54, 72…… The LCM of 9, 12, and 18 is 36.

72. Factors and Multiples Find the LCM of 5, 10 and 15. Do this on your own

73. Factors and Multiples Find the LCM of 5, 10 and 15. 5; 5, 10, 15, 25, 30, 35, 40…… 10; 10, 20, 30, 40…… 15; 15, 30, 45, 60…… The LCM of 5, 10, and 15 is 30.

74. Factors and Multiples Homework that does not include first and last name will no longer be graded.

75. Factors and Multiples Agenda Notes Homework – Homework Practice 1.1 Show all work! Due Friday, Aug 28 Accumulative Review 1 Due Sept 11