GCF

Greatest

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Factor

Common

Objectives

• generate a list of all factors of a given number
• given the lists of factors of two numbers, identify their GCF
• create a factor tree for a given number
• use the factor trees of two numbers to find their GCF

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Composite or Prime?

What's the difference?

7 = 1*7

24 = 1*24 2*12 3 * 8 4 * 6

A composite number has more than two factors. A prime number has only two factors: 1 and itself. 7 is prime. 24 is composite.

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List all factors of 36

36 = 1 * 36 2 * 18 3 * 12 4 * 9 6 * 6

Notice that 5 does not divide evenly into 36. 5 is not a factor of 36.

Quiz 1/10

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What are the common factors between 24 and 36?

36 = 1 * 36 2 * 18 3 * 12 4 * 9 6 * 6

Common Factors

24 = 1 * 24 2 * 12 3 * 8 4 * 6

24 and 36 have the following factors in common: 1, 2, 3, 4, 6, 12

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What is the greatest common factor for 24 and 36?

36 = 1 * 36 2 * 18 3 * 12 4 * 9 6 * 6

GCF

24 = 1 * 24 2 * 12 3 * 8 4 * 6

24 and 36 have the following factors in common: 1, 2, 3, 4, 6, 12 The Greatest Common Factor is 12.

Quiz 2/10

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What is this?

42

Factor Tree

14

3

2

7

Factor: Two numbers that are multiplied together. Factor Tree: A list of factors for a value where the lowest "branch" is a collection of prime factors.

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There's more than one way to start a factor tree.

42

Prime Factorization

14

2

7

42

3

7

6

2

3

42

21

3

7

2

What do you notice about the bottom branch?

The prime factorization of a number is the list of prime factors that multiply to the original value. You can find the prime factorization by looking at the bottom of all the branches. The prime factorization of 42 is 3*2*7. 42 = 3*2*7

Quiz 3/10

24

12

3

4

2

Quiz 4/10

100

4

Quiz 5/10

100

4

25

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You can use factor trees to find the GCF of 24 and 36.

24

8

3

2

4

Answer

36

12

3

3

4

Highlight the factors common between the trees.THENMultiply them to find the GCF.

3*4 = 12 The GCF for 24 and 36 is 12.

Quiz 6/10

24

8

3

2

4

42

7

6

2

3

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Find the GCF for 96 and 144.

Check Your Work

Step 1: Choose what method you will use Either factor trees or factor listsStep 2: Organize the factors for 96 and 144.Step 3: If you used factor trees, circle the common factors on each tree, then multiply the prime factorization.If you use a factor list, circle the common factors,then identify the GREATEST!

The GCF for 96 and 144 is 48.

DONE!

Real World Application!

You are making sandwiches for a fundraiser. You have 720 turkey slices and 480 cheese slices. If each sandwich is to have the same amount of turkey and cheese, what is the greatest number of sandwiches that can be made?

Remember to complete your Check for Understanding Bonus Point!

You Should be Able to

• generate a list of all factors of a given number
• given the lists of factors of two numbers, identify their GCF
• create a factor tree for a given number
• use the factor trees of two numbers to find their GCF