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Factors and Greatest Common Factors (GCF)

Factors and Greatest Common Factors (GCF). M6N1a, b. Factor. A number that is multiplied by another number to get a product. List all the factors of 24. EXAMPLE 1. 1,. 2,. 3,. 4,. 6,. 8,. 12,. 24. List all of the factors of 52. EXAMPLE 2. 1,. 2,. 4,. 13,. 26,. 52,.

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Factors and Greatest Common Factors (GCF)

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  1. Factors and Greatest Common Factors (GCF) M6N1a, b

  2. Factor • A number that is multiplied by another number to get a product.

  3. List all the factors of24 EXAMPLE 1 1, 2, 3, 4, 6, 8, 12, 24

  4. List all of the factors of 52 EXAMPLE 2 1, 2, 4, 13, 26, 52,

  5. List all the factors of 75 Your Turn 1, 3, 5, 15, 25, 75,

  6. List all the factors of35 YourTurn 1, 5, 7, 35,

  7. Greatest Common Factor(GCF) The largest factor that two or more numbers have in common

  8. Finding GCF Using the ladder method

  9. Find the GCF of60 and 84 EXAMPLE 1 Step 1: Find the smallest Prime Number that will go into each given number 60 84 30 42 15 21 5 7 Step 2: Multiply the numbers on the outside. 2 2 x 2 x 3 = 12 GCF = 12 2 3

  10. Find the GCF of 12, 18, and 60 EXAMPLE 2 12 18 60 6 9 30 2 3 10 2 x 3 = 6 GCF = 6 2 3

  11. Find the GCF of28 and 42 28 42 14 21 7 3 2 x 7 = 14 GCF = 14 Your Turn 2 7

  12. Find the GCF of 45, 18, and 27 Your Turn 45 18 27 15 6 9 5 2 3 3 x 3 = 9 GCF = 9 3 3

  13. Finding GCF By listing all the factors

  14. Find the GCF of 30 and 45 EXAMPLE 1 Step 1: List the factors of each number 1, 2, 3, 5, 6, 10, 15, 30 1, 3, 5, 9, 15, 45 Step 2: Identify the common factors Step 3: Write the largest factor the numbers have in common. GCF = 15

  15. Find the GCF of 16, 48, and 72 EXAMPLE 2 1, 2, 4, 8, 16 1, 2, 3, 4, 6, 8, 12, 24, 48 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 GCF = 8

  16. Find the GCF of36 and 72 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Your Turn GCF = 36

  17. Find the GCF of24, 48, and 84 Your Turn 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 GCF = 12

  18. PROBLEM SOLVING

  19. There are 40 girls and 32 boys who want to participate in the relay race. If each team must have the same number of girls and boys, what is the greatest number of teams that can race? How many boys and girls will be on each team? 8 teams with 5 girls and 4 boys each

  20. Carolyn has 24 bottles of shampoo, 36 tubes of hand lotion, and 60 bars of lavender soap to make gift baskets. She wants to have the same number of each item in every basket. What is the greatest number of baskets she can make without having any of the items left over? 12 baskets

  21. Ming has 15 quarters, 30 dimes, and 48 nickels. He wants to group his money so that each group has the same number of each coin. What is the greatest number of groups he can make? How many of each coin will be in each group? How much money will each group be worth? 3 groups with 5 quarters, 10 dimes, and 16 nickels each; $3.05

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