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 of24

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,

List all the factors of 75

Your Turn

1, 3, 5, 15, 25, 75,

List all the factors of35

Your Turn

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 of60 and 84

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.

22

3

2 x 2 x 3 = 12

GCF = 12

EXAMPLE 1

Find the GCF of 12, 18, and 60

12 18 60

6 9 30

2 3 10

2 x 3 = 6

GCF = 6

2

3

EXAMPLE 2

Find the GCF of28 and 42

28 42

14 21

7 3

2 x 7 = 14

GCF = 14

27

Your Turn

Find the GCF of 45, 18, and 27

45 18 27

15 6 9

5 2 3

3 x 3 = 9

GCF = 9

Your Turn

33

Finding GCF

By listing all the factors

Find the GCF of 30 and 45

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

EXAMPLE 1

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

EXAMPLE 2

GCF = 8

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

Find the GCF of24, 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

Your Turn

GCF = 12

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