GCF Word Problems: 8 Worked Examples with Clear Explanations

Practice greatest common factor word problems about groups, gift bags, tiles, ribbons and teams, with a simple checklist for spotting when to use the GCF.

By the Dayob Editorial Team · Updated · 3 min read

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Try the GCF Calculator – Enter two or more whole numbers to get their greatest common factor, least common multiple, prime factorizations and the Euclidean algorithm worked out.

GCF word problems almost always ask you to split two or more amounts into the largest number of identical groups (or the largest equal pieces) with nothing left over. If you see those ideas, reach for the greatest common factor. If the problem instead asks when things line up again, it probably needs the LCM; see GCF vs. LCM.

1. Gift bags

You have 48 pencils and 36 erasers. What is the greatest number of identical gift bags you can make using all of them?

GCF(48, 36) = 12. Twelve bags, each with 4 pencils and 3 erasers.

2. Ribbon pieces

Two ribbons are 84 cm and 126 cm long. You want to cut both into pieces of equal length, as long as possible, with no waste.

GCF(84, 126) = 42. Each piece is 42 cm: 2 from the first ribbon and 3 from the second.

3. Square tiles

A floor is 270 cm by 360 cm. What is the largest square tile that covers it exactly, without cutting?

GCF(270, 360) = 90. Tiles 90 cm on a side: 3 × 4 = 12 tiles. In practice, grout gaps and real tile sizes make this a math exercise rather than a buying guide; for real flooring, see the square footage calculator.

4. Teams

A club has 24 girls and 32 boys. It wants equal teams, each with the same number of girls and the same number of boys. What is the most teams possible?

GCF(24, 32) = 8. Eight teams, each with 3 girls and 4 boys.

5. Three quantities

A baker has 60 chocolate, 84 vanilla and 108 lemon cookies to pack into identical boxes using every cookie.

GCF(60, 84, 108) = 12. Twelve boxes with 5 chocolate, 7 vanilla and 9 lemon cookies each. The GCF calculator accepts any number of values.

6. Garden rows

A gardener has 45 tomato plants and 75 pepper plants and wants rows with the same number of plants, each row containing only one type. What is the largest number of plants per row?

GCF(45, 75) = 15. Rows of 15: 3 rows of tomatoes and 5 of peppers.

7. Fabric squares

A quilter has a piece of fabric 54 inches by 72 inches and wants to cut it into the largest identical squares with no leftover.

GCF(54, 72) = 18. Squares of 18 inches: 3 × 4 = 12 squares.

8. When the answer is 1

You have 13 apples and 20 oranges. How many identical fruit bowls can you make using all the fruit?

GCF(13, 20) = 1. Only one bowl, containing everything, because 13 is prime and doesn't divide 20. That's a valid answer, and a useful reminder that some numbers simply don't share factors.

Checklist for GCF problems

  • Are you dividing existing amounts (not building up to a new total)?
  • Must every group or piece be identical?
  • Must everything be used, with nothing left over?
  • Does the problem ask for the largest or greatest?

Four yeses mean GCF. After finding it, always divide each amount by the GCF to describe what's in each group; many teachers expect that part of the answer too.

Further reading from official sources

More gcf guides

A student writing formulas on a chalkboardGCF vs. LCM: What's the Difference and When to Use EachThe greatest common factor and least common multiple are easy to confuse. Learn what each one means, how they're related, and which one a word problem needs.3 min readA man standing in front of a chalkboard covered in equationsThe Euclidean Algorithm: The Fastest Way to Find the GCFHow Euclid's division method finds the greatest common factor of large numbers in a few steps, why it works, and how to extend it to three or more numbers.3 min readA young boy writing complex formulas on a chalkboardPrime Factorization: Factor Trees, Division Ladders and Divisibility RulesBreak any number into prime factors using factor trees or the ladder method, with divisibility shortcuts and examples of using primes to find the GCF and LCM.3 min read