Factors and Greatest Common Factors GCF M 6

Factors and Greatest Common Factors (GCF) M 6 N 1 a, b

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

1 E PL List all the factors of 24 M A X E 1, 2, 3, 4, 6, 8, 12, 24

List all of the factors of 2 52 E L P M A X E 1, 2, 4, 13, 26, 52,

List all the factors of rn 75 u r. T u o Y 1, 3, 5, 15, 25, 75,

Yo rn u T ur List all the factors of 35 1, 5, 7, 35,

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

Finding GCF Using the ladder method

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

Find the GCF of 12, 18, and 60 2 12 18 60 9 30 3 6 2 3 10 2 x 3=6 GCF = 6 EXA MPL E 2

Find the GCF of 28 and 42 Your Tu rn 2 28 42 7 14 21 7 3 2 x 7 = 14 GCF = 14

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

Finding GCF By listing all the factors

Find the GCF of 30 and 45 EX AM PL E 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

Find the GCF of 16, 48, and 72 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 EXA MPL E 2

Find the GCF of 36 and 72 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 GCF = 36 Yo ur Tu rn

Find the GCF of 24, 48, and 84 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 You r Tu rn

PROBLEM SOLVING

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

• 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

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