GCF
LCM
Factoring out the GCF
Word Problems
100

Find the GCF (21, 28)

7

100

Find the LCM (12, 18)

36

100

Which of the properties of addition does the following math expression demonstrate?

9+0 = 9

100

Apply the distributive property to factor out the greatest common factor.

3+21

3(1+7)

100

Jazmin is completing an art project. She has two pieces of construction paper. The first piece is 44 cm wide and the second piece is 33 cm wide.

Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible.

How wide should Jazmin cut each strip?

11 cm (GCF)

200

Find the GCF (8, 14, 26)

2

200

Find the LCM (8, 9)

72

200

Which of the properties of addition does the following expression demonstrate?

102+493 = 493+102

200

Apply the distributive property to factor out the greatest common factor.

20+24

4(5+6)

200

Peter's Party Zone sells cups in packages of 6 and plates in packages of 8.

Shaniya is hosting a birthday party for her little sister and wants to have the same number of each item.

What is the least number of packages of plates Shaniya needs to buy?

3 packages of plates (LCM)

3 packages of plates give 24 plates

300

Find the GCF (32, 48, 30, 2)

2

300

Find the LCM (10, 4, 8)

40

300

Which of the properties of addition does the following expression demonstrate?

(7+2) +9 = 7+(2+9)

300

Apply the distributive property to factor out the greatest common factor.

33+44

11(3+4)

300

Ronald and Tim both did their laundry today. Ronald does laundry every 6 days and Tim does laundry every 9 days.

How many days will it be until Ronald and Tim both do laundry on the same day again?

18 days (LCM)

400

Use the distributive property to factor out the GCF of 35+50

5(7+10)

400

Find the LCM (12, 5, 3)

60

400

Which of the properties of multiplication does the following math expression demonstrate?

9x(67x2) = (9x67)x2

Associative Property of Multiplication

400

Apply the distributive property to factor out the greatest common factor.

25+30

5(5+6)

400

Abe is going to plant 54 oak trees and 27 pine trees.

Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree.

What is the greatest number of trees Abe can have in each row?

27 trees (GCF)

500

Use the distributive property to factor out the GCF of 6+33

3(2+11)

500

Find the LCM (4, 8, 9, 6)

72

500

Which of the properties of multiplication does the following expression demonstrate?

6(2+4) = 6(2)+6(4)

Distributive Property of Multiplication

500

Apply the distributive property to factor out the greatest common factor.

63+45

9(7+5)

500

Rafaela is a physical education teacher and has 25 girls and 35 boys in her class.

She wants to divide the class into teams of the same size, where each team has the same number of girls and the same number of boys.

If Rafaela creates the greatest number of teams possible, how many boys will be on each team?

7 boys on each team (GCF)

5 teams with 7 boys and 5 girls each

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