+

Find greatest common factor and least common multiple; express the sum of numbers with a common factor as a multiple of a sum of numbers with no common factor

Common Core 6.NS.B.4

+Warm Up

List all of the ways you can write the product of the number:

72

1 x 72

2 x 36

3 x 24

4 x 18

6 x 12

8 x 9

Can you list all the different ways Elly can make treat bags if each treat bag has the

same amount of mints inside?

Elly is making treat bags for her class party.

Elly brought 20 mints.

In this lesson you will learn how to answer word problems and

find the GCF by listing factor pairs.

Let’s Review

Both 3 and 4 are factors of 12.

Factors are numbers multiplied together to equal a product.

3 x 4 = 12

For example:

3 x 4 is a factor pair

Let’s Review

The product 12 has these 6 factor pairs.

1 x 122 x 63 x 44 x 36 x 212 x 1

Core Lesson

La’Nya has 16 pieces of gum. List all the different ways she can make treat bags if each treat bag has the same

amount of gum inside.

Example # 1:

Core Lesson

16

La’Nya can make one bag with 16 pieces of gum, or she can make 16 bags with 1 piece of gum in each.

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1or

Core Lesson

La’Nya can make 2 bags with 8 pieces of gum in each, or she can make 8 bags with 2 pieces

of gum in each.

88

or

2 2

2 2

2 2

2 2

Core Lesson

La’Nya can make 4 bags with 4 pieces of gum in each, or she can make 4 bags with 4 pieces

of gum in each. Same thing!

4

4 4

4 4

4 4

4or

Core Lesson

# of bags

# of treats in each bag

1 x 16

2 x 8

4 x 4

8 x 2

16 x 1

List all the different ways La’Nya can make treat bags.

Erica and Craig are making treat bags for their class party.

Erica brought 32 pieces of gum.

Craig brought 40 chocolates.

What is the greatest number

of equal treat bags they can make?

Core Lesson

3 steps to finding the Greatest Common Factor

1. List the factor pairs.

2. Identify the common factors.

3. Find the biggest common factor. That is the Greatest Common Factor (GCF)

Core Lesson

Find the greatest common factor of 32 and 40.

Factor Pairs of 40

1 x 40

2 x 20

4 x 10

5 x 8

8 x 5

10 x 4

20 x 2

40 x 13. Find GCF 1, 2, 4, 8

Factor Pairs of 32

1 x 32

2 x 16

4 x 8

8 x 4

16 x 2

32 x 1

1. List factor pairs

2. Find common factors

Core Lesson

Erica brought 32 pieces of gum.

Factor Pairs of 32# of bags # of

treats

1 x 32

2 x 16

4 x 8

8 x 4

16 x 2

32 x 1

4 gum 4 gum 4 gum 4 gum

4 gum 4 gum 4 gum 4 gum

Core Lesson

Factor Pairs of 40

# of bags

# of treats

1 x 40

2 x 20

4 x 10

5 x 8

8 x 5

10 x 4

20 x 2

40 x 1

Craig brought 40 chocolates.

5 chocolate

s

5 chocolates 5

chocolates

5 chocolate

s

5 chocolate

s5

chocolates

5 chocolate

s5

chocolates

Core Lesson

5 mints 5 mints 5 mints 5 mints 5 mints 5 mints 5 mints 5 mints

The greatest number of equal treat bags Jon and Elly can make is 8.

4 gum 4 gum4 gum 4 gum4 gum 4 gum4 gum 4 gum

5 mints5 mints 5 mints 5 mints5 mints 5 mints5 mints 5 mints4 gum 4 gum 4 gum4 gum 4 gum4 gum 4 gum4 gum

Jon and Elly can combine bags.

Core Lesson

Noah bought a bag of 56 Jolly Ranchers.

Can you list all the different ways he can make treat bags if each treat bag has the same

amount of jolly ranchers inside?

Core Lesson

That makes 6 ways Noah can make treat bags.

1 x 202 x 104 x 55 x 410 x 220 x 1

Core Lesson