Greatest Common Factor Word Problems- Free Worksheet with Solutions

What You Actually Need to Know About GCF Word Problems

GCF word problems look intimidating on paper. They pile on real-world scenarios—dividing supplies, grouping items, sharing equally—that obscure the actual math underneath. Once you strip away the story, you're just finding the biggest number that divides evenly into everything.

This guide cuts through the confusion. You'll get a step-by-step approach to crack any GCF word problem, worked examples, and a free practice worksheet with full solutions at the end.

Quick GCF Refresher

The Greatest Common Factor (also called Greatest Common Divisor) is the largest number that divides into two or more numbers without leaving a remainder.

Example: GCF of 12 and 18

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Common factors: 1, 2, 3, 6
• GCF = 6

You can also use prime factorization or the Euclidean algorithm for larger numbers. Pick whichever method feels faster for the numbers you're working with.

How to Solve Any GCF Word Problem

Most students freeze when they see a word problem. Here's the fix:

Step 1: Identify What You're Dividing

Read the problem once. Find the quantities being split up or grouped. These are your numbers.

Step 2: Find the GCF

Calculate the greatest common factor of those numbers using your preferred method.

Step 3: Answer What the Problem Actually Asks

The GCF isn't always the final answer. Sometimes it tells you how many groups you can make, or how many items go in each group. Read carefully.

Step 4: Check Your Work

Multiply your answer back out. Does it divide evenly into the original quantities? If not, something went wrong.

Worked Examples

Example 1: Dividing Supplies

"Maria has 24 apples and 36 oranges. She wants to make identical fruit baskets with no fruit left over. What is the greatest number of baskets she can make?"

Step 1: Numbers are 24 and 36.

Step 2: GCF(24, 36) = 12.

Step 3: She can make 12 baskets.

Check: 24 ÷ 12 = 2 apples per basket. 36 ÷ 12 = 3 oranges per basket. Nothing left over. Done.

Example 2: Grouping Objects

"A teacher has 45 markers and 60 pencils. She wants to distribute them equally into containers. Each container gets the same number of markers and the same number of pencils. What is the maximum number of containers?"

Step 1: Numbers are 45 and 60.

Step 2: GCF(45, 60) = 15.

Step 3: Maximum containers = 15.

Check: 45 ÷ 15 = 3 markers per container. 60 ÷ 15 = 4 pencils per container. Clean division. Works.

Example 3: Three Numbers

"A baker has 48 chocolate chips, 72 raisins, and 96 walnuts. He wants to make identical snack bags with no ingredients left over. What is the greatest number of bags?"

Step 1: Numbers are 48, 72, and 96.

Step 2: GCF(48, 72, 96) = 24.

Step 3: Maximum bags = 24.

Check: 48 ÷ 24 = 2 chocolate chips per bag. 72 ÷ 24 = 3 raisins per bag. 96 ÷ 24 = 4 walnuts per bag. Everything divides evenly.

GCF vs. LCM in Word Problems: Don't Mix Them Up

This trips up almost everyone. Here's the difference fast:

If the problem says "largest number of equal groups" or "greatest number of items per group" with no remainder → GCF.

If the problem says "next time they meet," "both events happen at the same time," or "find the common multiple" → LCM.

Common Mistakes That Kill Your Score

• Finding the LCM instead of the GCF — Read the question twice before you calculate.
• Not checking your answer — Always verify that your GCF divides evenly into all numbers given.
• Confusing the GCF with the answer — Sometimes the GCF is the number of groups. Sometimes it's items per group. The question tells you which.
• Skipping the story — Don't ignore the context. The words tell you what the math represents.

GCF Word Problems Practice Worksheet

Try these problems. Full solutions are at the bottom.

Problems

1. A craft store has 30 red beads and 45 blue beads. If the beads are divided equally into necklaces with no beads left over, what is the greatest number of necklaces that can be made?
2. Three buses hold 24, 36, and 48 students. The students need to be split into equal groups with no one left out. What is the maximum group size?
3. Jake has 56 baseball cards and 84 basketball cards. He wants to sort them into binders with the same number of cards per binder. What is the greatest number of binders he can use?
4. A gardener has 64 tulip bulbs, 80 daffodil bulbs, and 96 sunflower seeds. She plants them in rows with each row containing only one type, and all rows have the same number of plants. What is the maximum number of rows she can create?
5. Two teachers have 42 worksheets and 56 quizzes. They want to make identical packets with no papers left over. What is the greatest number of packets they can make?

Solutions to Practice Problems

Problem 1

GCF(30, 45) = 15. The greatest number of necklaces is 15.

Check: 30 ÷ 15 = 2 red beads per necklace. 45 ÷ 15 = 3 blue beads per necklace.

Problem 2

GCF(24, 36, 48) = 12. The maximum group size is 12 students.

Check: 24 ÷ 12 = 2 students from first bus. 36 ÷ 12 = 3 from second. 48 ÷ 12 = 4 from third.

Problem 3

GCF(56, 84) = 28. The greatest number of binders is 28.

Check: 56 ÷ 28 = 2 baseball cards per binder. 84 ÷ 28 = 3 basketball cards per binder.

Problem 4

GCF(64, 80, 96) = 16. The maximum number of rows is 16.

Check: 64 ÷ 16 = 4 tulips per row. 80 ÷ 16 = 5 daffodils per row. 96 ÷ 16 = 6 sunflowers per row.

Problem 5

GCF(42, 56) = 14. The greatest number of packets is 14.

Check: 42 ÷ 14 = 3 worksheets per packet. 56 ÷ 14 = 4 quizzes per packet.

Download the Worksheet

Need more practice? Get the printable version with 10 additional problems and a complete answer key.

The worksheet covers two-number GCF problems, three-number GCF problems, and mixed difficulty. Print it out, work through it, check your answers.

That's it. No summary. No motivational send-off. You got the tools. Use them.