GCF

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Greatest

Common

Factor

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?

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

7 = 1*7

What's the difference?

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List all factors of 36

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

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What are the common factors between 24 and 36?

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

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

Common Factors

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What is the greatest common factor for 24 and 36?

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

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

GCF

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What is this?

42

14

Factor Tree

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

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42

42

42

Prime Factorization

14

21

What do you notice about the bottom branch?

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24

12

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100

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100

25

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

36

24

Highlight the factors common between the trees. THEN Multiply them to find the GCF.

12

Answer

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42

24

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Find the GCF for 96 and 144.

Step 1: Choose what method you will use Either factor trees or factor lists Step 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!

Check Your Work

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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?

DONE!

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