Tuesday, Sept 3 Lesson 1.1 Greatest Common Factors
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Factors and Multiples Objective: To find the Greatest Common
Factor.
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Factors and Multiples
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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).
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Factors and Multiples Greatest Common Factor What does greatest
mean?
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Factors and Multiples Greatest Common Factor What does common
mean?
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Factors and Multiples Greatest Common Factor What does factor
mean?
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Factors and Multiples Greatest Common Factor would be the
largest number that is in all rainbow factors.
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Factors and Multiples There are two ways to find the GCF
-Factor List (Factor Rainbows) -Factor Trees
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Factors and Multiples What is the GCF of 8 and 12?
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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)
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Factors and Multiples What is the GCF of 8 and 12? Step 1 List
the factors for each number. 8:1, 2, 4, 8
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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
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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.
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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.
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Factors and Multiples What is the GCF of 20 and 32?
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Factors and Multiples What is the GCF of 20 and 32? Step 1
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Factors and Multiples What is the GCF of 20 and 32? Step 1 list
the factors for each number. (Create a factor list)
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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
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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
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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
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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.
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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.
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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?
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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?
Slide 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?
Slide 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?
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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?
Slide 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?
Slide 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?
Slide 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?
Slide 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?
Slide 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?
Slide 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.
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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?
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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?
Slide 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, 15 20 ; 1, 2, 4, 5, 10,
15 Step 2?
Slide 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, 15 20 ; 1, 2, 4, 5, 10,
20
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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?
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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
Slide 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?
Slide 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
Slide 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?
Slide 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
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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?
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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?
Slide 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
Slide 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?
Slide 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
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Factors and Multiples We can also find the GCF with factor
trees.
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Factors and Multiples What is the GCF of 8 and 12?
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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
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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.
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Factors and Multiples What is the GCF of 8 and 12? 8 12 2 2 2
3
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Factors and Multiples What is the GCF of 8 and 12? Step 3
Multiply the numbers in the intersection. 812 2 2 2 3
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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).
812 2 2 2 3
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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?
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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.
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Factors and Multiples Before you try either method, try and use
Mr. Averys GCF rule. Mr. Averys GCF Rule If the smaller number goes
into the larger number(s), the smaller number is the GCF.
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Factors and Multiples What is the GCF of 6 and 12?
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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
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Factors and Multiples What is the GCF of 18 and 30.
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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
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Factors and Multiples What is the GCF of 32 and 48.
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Factors and Multiples What is the GCF of 32 and 48. 32; 1, 2,
4, 8, 16, 32 48; 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
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Factors and Multiples What is the GCF of 22 and 66.
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Factors and Multiples What is the GCF of 22 and 66. Mr. Averys
Rule - Since 22 x 3 = 66 22 is the GCF.
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Factors and Multiples What is the GCF of any two prime
numbers?
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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
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Factors and Multiples Agenda Notes Homework Homework Practice
1-1 Due Wednesday, Sept 4