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Greatest Common Greatest Common FactorFactor

Greatest Common Greatest Common FactorFactor

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Warm-Up!1. 5 2.52. 152 x 1003. Is 171 divisible by 3? How do you know?4. What rule tells us if a number is divisible by 6? By 9?5. Make a factor tree for 60

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Let’s review!Find the mean of the data set

below: 69, 73, 75, 58, 85

What is the median of the data set above?

What is the range?

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What is Greatest Common Factor (GCF)?

GCF: The largest factor shared between two or more numbers

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Ways to find the GCF

• Make a list of factors for each of

the numbers

• Use Prime Factorization

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Let’s list the factors!24

1, 2, 3, 4, 6, 8, 12, 24

361, 2, 3, 4, 6, 9, 12, 18, 36

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Which factors do 24 and 36 have in common?

241, 2, 3, 4, 6, 8, 12, 24

361, 2, 3, 4, 6, 9, 12, 18, 36

The largest factor they both have in common is 12!

GCF: 12

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Let’s try another example!

9 1, 3, 9

12 1, 2, 3, 4, 6, 12

The greatest common factor is 3

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You try!

Find the GCF by listing the factors:A. 25 15

B. 16 20

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Find GCF by using prime factorization

Step One: Make a factor tree for each numberEx:

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Step 2Circle the prime factors in common

54: 2, 3, 3, 3

81: 3, 3, 3, 3

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Step 3Multiply the common prime factors

Notice that 54 and 81 share three 3’s in common.

To get our answer we will multiply 3 x 3 x 3.

Our GCF is 27!

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Let’s look at another example!

36 and 24 share two 2’s and one 3 in common.

GCF: 12

36: 2, 2, 3, 3 24: 2, 2, 2, 3

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You try!

Find the GCF by using prime factorization

75 50

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Find the GCF by using Prime Factorization

56 84

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Break!

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Puzzlehttp://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/clover3805.html

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Word Problems 1a. The Dance Team has 16 dancers dressed in

red, 24 dressed in white, and 40 dressed in blue. The head of the team wants to have the same number of dancers in each row. Each row will have dancers with the same color. What is the greatest number of dancers in a row?

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Word Problems 1b. Marie wants to make goodie bags for

her birthday party. She wants to put the same number of goodies in each bag. She has 48 candy bars, 80 lollipops, and 32 bottles of bubbles. What’s the largest number of goodie bags she can make?

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Assessment1. Name two ways to find GCF2. List the factors to find the GCF

a. 48, 24b. 27, 39c. 56, 32, 72

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3. Find the GCF by using prime factorizationa. 90 30

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Assessment

3b. 144 108

4. If two numbers are prime, what will their GCF be?

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5. Use either method to find GCFa. 35, 14, 49

b. 256, 144, 88

Assessment

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Today we learned:• Greatest Common Factor (GCF) is the

largest factor that two or more numbers have in common

• There are two ways to find GCF:– Make a list of factors– Use Prime Factorization