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# Greatest Common Factor (GCF)

Greatest Common Factor (GCF). Created by: Mrs. J Couch. GCF. Finding the greatest of the common factors of two (or more) numbers. Example. Find the GCF of 20 and 24 using prime factorization. 20 = 2 x 2 x 5 24 = 2 x 2 x 2 x 3

## Greatest Common Factor (GCF)

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1. Greatest Common Factor (GCF) Created by: Mrs. J Couch

2. GCF • Finding the greatest of the common factors of two (or more) numbers

3. Example • Find the GCF of 20 and 24 using prime factorization. 20 = 2 x 2 x 5 24 = 2 x 2 x 2 x 3 -Identify all commonfactors in the factorization of 20 and 24. 20 = 2 x 2 x 5 24 = 2 x 2 x 2 x 3 The greatestcommon factor of 20 and 24 is the product of all commonfactors 2 x 2 = 4

4. Finding GCF using Ladder Method Divide out all the common factors down the left side. 2 24 60 What number (smallest prime #) goes into both 24 and 60? Does any # besides 1 go into both 12 and 30? 2 12 30 How about 6 and 15? Anything else? 3 6 15 No? You’re done. Multiply left side Only to get GCF 2 5 GCF= 2 * 2 * 3 = 12

5. Practice • Find the greatest common factor of 24 and 18.

6. Practice • Find the greatest common factor of 96 and 72.

7. Practice • Find the greatest common factor of 32 and 52.

8. Practice • Xavier is visiting the hospital in order to give stuffed animals and books to sick children. He has 16 stuffed animals and 20 books to give. If he wants to give the same combination of stuffed animals and books to each child, with no gifts left over, what is the greatest number of children Xavier can give gifts to? (Remember to give your answer using a complete sentence)

9. Practice • Find the GCF of 12 and 36

10. Practice • Two students are having a party. They want to make treat bags for their guests. They want each bag to be identical with nothing leftover. They have 36 Silly Bandz and 72 pieces of bubble gum to put in the bags. What is the greatest number of treat bags they can make and how many of each item will be in each treat bag?

11. Practice • Mitzi is making trail mix out of 48 bags of nuts and 32 bags of dried cranberries. She wants each new portion of trail mix to be identical containing the same combination of nuts and cranberries with nothing left over. What is the greatest number of portions of trail mix Mitzi can make and how much of each ingredient will be in each portion?

12. Connection to Distributive Property • How does finding the greatest common factor help you in the distributive property? Ex. Write a number sentence for 12 + 18 -think about the common factors of 12 and 18 Common factors: 1, 2, 3, 6 2 (6 + 9) Use the common factors to write the number sentence 3 ( + ) 6 ( + )

13. Practice with Distributive Property • Write a number sentence (using the GCF) for: • 42 + 36 • 18 + 25 • 50 + 60

14. Exit Slip • Find the GCF of 27 and 36 • Find the GCF of 12 and 22 • Find the GCF of 42 and 80 • Write a number sentence (using the GCF) for 20 + 25

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