Greatest Common Factor Word Problems

1.) Students in the drama club had a party. They had 185 mini sandwiches and 148 brownies. The drama club shared the sandwiches and brownies equally. How many members could there be?

2.) A farmer decided to divide his sheep and cattle among his sons. He had 45 head of sheep and 72 head of cattle. The division of animals came out even. What is the largest possible number of sons the farmer could have?

3.) In a parade, one school band will march directly behind one another. All rows must have the same number of students. The first band has 36 students, and the second band has 60 students. What is the greatest number of students who can be in each row?

4.) Jason is trying to make picnic lunches. He has 12 sandwiches, 18 apples and 30 pieces of candy. How many lunches can he make if he wants each lunch to have the same number of each kind of food and use all of the food?

5.) 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?

6.) Kim packed 6 boxes with identical supplies. It was the greatest number she could pack and use all the supplies. Which of these is her supply list?
a. 24 pencils, 36 pens, 10 rulers
b. 12 rulers, 30 pencils, 45 pens
c. 42 pencils, 18 rulers, 72 pens
d. 60 pens, 54 pencils, 32 rulers

GCF Practice
•_____Pam is making fruit baskets. She has 30 apples, 24 bananas, and 12 oranges. What is the greatest number of baskets she can
make if each type of fruit is distributed equally among the baskets?

•_____Jared has 12 jars of grape jam, 16 jars of strawberry jam and 24 jars of raspberry jam. He wants to place them into the greatest possible number of boxes so that each box has the same number of jars of each kind of jam. How many boxes does he need?

•_____There are 14 girls and 21 boys in Ms. J's gym class. To play a certain game, the students must form teams. Each team must have
the same number of girls and the same number of boys. What is the greatest number of teams Ms. J can make if every student is on a
team?

•_____String cheese sticks are sold in packages of 10 and celery sticks in packs of 15. Mr. Sobrino wants to give each of the 30
students one string cheese stick and one celery stick. What is the least number of packs he should buy so there are none left over?

•_____Mr. K makes balloon arrangements. He has 32 blue balloons, 24 yellow balloons and 16 white balloons. Each arrangement must
have an equal number of each color. What is the greatest number of arrangements that Mr. K can make if each balloon is used?

•_____Pencils are sold in packs of 12 and erasers in packs of 9. A teacher wants to give each of 36 students a pencil and an eraser.
What is the least number of packs he should buy so that there are none left over?