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Tuesday, Sept 3 Lesson 1.1 Greatest Common Factors.

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1 Tuesday, Sept 3 Lesson 1.1 Greatest Common Factors

2 Factors and Multiples Objective: To find the Greatest Common Factor.

3 Factors and Multiples

4 A common factor is a number that is a factor of two or more numbers. The greatest of the common factors of two or more numbers is called the greatest common factor (GCF).

5 Factors and Multiples Greatest Common Factor – What does “greatest” mean?

6 Factors and Multiples Greatest Common Factor – What does “common” mean?

7 Factors and Multiples Greatest Common Factor – What does “factor” mean?

8 Factors and Multiples Greatest Common Factor would be the largest number that is in all rainbow factors.

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

10 Factors and Multiples What is the GCF of 8 and 12?

11 Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – List the factors for each number. (Create a factor list)

12 Factors and Multiples What is the GCF of 8 and 12? Step 1 – List the factors for each number. 8:1, 2, 4, 8

13 Factors and Multiples What is the GCF of 8 and 12? Step 1 – List the factors for each number. 8:1, 2, 4, 8 12:1,2,3,4,6,12

14 Factors and Multiples What is the GCF of 8 and 12? 8:1, 2, 4, 8 12:1,2,3,4,6,12 Step 2 – Determine the greatest number that is in each list.

15 Factors and Multiples What is the GCF of 8 and 12? 8:1, 2, 4, 8 12:1,2,3,4,6,12 Step 2 – Determine the greatest number that is in each list. The GCF of 8 and 12 is 4.

16 Factors and Multiples What is the GCF of 20 and 32?

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

18 Factors and Multiples What is the GCF of 20 and 32? Step 1 – list the factors for each number. (Create a factor list)

19 Factors and Multiples What is the GCF of 20 and 32? Step 1 – list the factors for each number. 20: 1,2,4,5,10,20

20 Factors and Multiples What is the GCF of 20 and 32? Step 1 – list the factors for each number. 20: 1,2,4,5,10,20 32:1,2,4,8,16,32

21 Factors and Multiples What is the GCF of 20 and 32? Step 1 – list the factors for each number. 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 Step 2 –

22 Factors and Multiples What is the GCF of 20 and 32? Step 1 – list the factors for each number. 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 Step 2 – Determine the greatest number that is in each list.

23 Factors and Multiples What is the GCF of 20 and 32? Step 1 – list the factors for each number. 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 Step 2 – Determine the greatest number that is in each list. The GCF of 20 and 32 is 4.

24 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row?

25 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with one slice of cake in each row?

26 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with one slice of cake in each row? Yes, we can have a row with one-slice of cake. But is it the greatest (largest) number of slices we can have in each row?

27 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with two slices of cake in each row?

28 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with two slices of cake in each row? No, if each row has to have an equal number of servings, how many two slice rows could we make with 15 red velvet slices?

29 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with three slices of cake in each row?

30 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with three slices of cake in each row? No, if each row has to have an equal number of servings, how many three slice rows could we make with 10 marble and 20 chocolate slices?

31 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with four slices of cake in each row?

32 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with four slices of cake in each row? No, if each row has to have an equal number of servings, how many four slice rows could we make with 10 marble and 15 red velvet slices?

33 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with five slices of cake in each row?

34 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with five slices of cake in each row? Yes, if each row has to have an equal number of servings, we would have 2 rows marble, 3 rows of red velvet slices and 4 rows of chocolate.

35 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Is there an easier way to do this?

36 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Is there an easier way to do this? Yes, we can find the GCF of 10, 15 and 20. Step 1?

37 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? 10; 1, 2, 5, 10 15; 1, 3, 5, ; 1, 2, 4, 5, 10, 15 Step 2?

38 Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? 10; 1, 2, 5, 10 15; 1, 3, 5, ; 1, 2, 4, 5, 10, 20

39 Factors and Multiples Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has the same number of carrot and celery sticks. What is the greatest number of bags he can put together? Step 1?

40 Factors and Multiples Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has the same number of carrot and celery sticks. What is the greatest number of bags he can put together? 60: 1,2,3,4,5,6,10,15,20,30,60

41 Factors and Multiples Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has the same number of carrot and celery sticks. What is the greatest number of bags he can put together? 60: 1,2,3,4,5,6,10,15,20,30,60 42: 1,2,3,6,7,14, 21,42 Step 2?

42 Factors and Multiples Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has the same number of carrot and celery sticks. What is the greatest number of bags he can put together? 60: 1,2,3,4,5,6,10,15,20,30,60 42: 1,2,3,6,7,14, 21,42

43 Factors and Multiples Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has the same number of carrot and celery sticks. What is the greatest number of bags he can put together? If we had 6 bags, how many carrots and celery sticks would be in each bag?

44 Factors and Multiples Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has the same number of carrot and celery sticks. What is the greatest number of bags he can put together? If we had 6 bags, how many carrots and celery sticks would be in each bag? 60 carrot sticks ÷ 6 bags = 10 in each bag 42 celery sticks ÷ 6 bags = 7 in each bag

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? Step 1?

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? 49: 1, 7, 49 42: 1, 2, 6, 7, 21, 42 21: 1, 3, 7, 21 Step 2?

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? 49: 1, 7, 49 42: 1, 2, 6, 7, 21, 42 21: 1, 3, 7, 21

48 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 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

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

51 Factors and Multiples What is the GCF of 8 and 12?

52 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

53 Factors and Multiples What is the GCF of 8 and 12? 812 / \ / \ 2 x 4 2 x 6 I / \ I / \ 2 x 2 x 2 2 x 2 x 3 Step 2 – Make a Venn Diagram with the prime factors.

54 Factors and Multiples What is the GCF of 8 and 12?

55 Factors and Multiples What is the GCF of 8 and 12? Step 3 – Multiply the numbers in the intersection

56 Factors and Multiples What is the GCF of 8 and 12? Step 3 – Multiply the numbers in the intersection. The GCF is 4 ( 2 x 2)

57 Factors and Multiples Since the factor tree method is longer, in what situations would you choose to use this method, rather than the factor list method?

58 Factors and Multiples Since the factor tree method is longer, in what situations would you choose to use this method, rather than the factor list method? If the number has a long factor list.

59 Factors and Multiples Before you try either method, try and use Mr. Avery’s GCF rule. Mr. Avery’s GCF Rule – If the smaller number goes into the larger number(s), the smaller number is the GCF.

60 Factors and Multiples What is the GCF of 6 and 12?

61 Factors and Multiples What is the GCF of 6 and 12? Since 6 goes into 12, then 6 is the GCF. You can prove this by factor lists. 6; 1, 2,3, 6 12; 1, 2, 3, 4, 6, 12

62 Factors and Multiples What is the GCF of 18 and 30.

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

64 Factors and Multiples What is the GCF of 32 and 48.

65 Factors and Multiples What is the GCF of 32 and ; 1, 2, 4, 8, 16, 32 48; 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

66 Factors and Multiples What is the GCF of 22 and 66.

67 Factors and Multiples What is the GCF of 22 and 66. Mr. Avery’s Rule - Since 22 x 3 = is the GCF.

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

69 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

70 Factors and Multiples Agenda Notes Homework – Homework Practice 1-1 Due Wednesday, Sept 4


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