Worksheets · Pre-Algebra

Greatest common factor worksheet

Break each number into its prime factors and take everything they share. What you are left with is the largest number that goes into all of them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Greatest Common Factor

Date Period

Find each greatest common factor, or solve each problem.

  1. Find the greatest common factor

    Find the GCF of 12 and 18.
  2. Find the GCF of 8 and 10.
  3. Find the GCF of 12 and 9.
  4. Find the GCF of 24 and 20.
  5. Find the GCF of 21 and 35.
  1. Solve GCF word problems

    56 granola bars and 40 juice boxes are split into identical bags with none left over. What is the greatest number of bags?
  2. 35 red roses and 20 white roses are split into identical bags with none left over. What is the greatest number of bags?
  3. 6 bouncy balls and 9 stickers are split into identical bags with none left over. What is the greatest number of bags?
  4. 88 pencils and 55 erasers are split into identical bags with none left over. What is the greatest number of bags?
  5. 36 pencils and 84 erasers are split into identical bags with none left over. What is the greatest number of bags?
  1. Find the GCF of monomials

    Find the GCF of 7x3 and 14x.
  2. Find the GCF of 12a and 60a.
  3. Find the GCF of 48a2 and 8a3.
  4. Find the GCF of 3m and 3m4.
  5. Find the GCF of 24x and 24x5.
  1. Use the GCF to factor a sum

    Use the GCF to write 5+25 as a product.
  2. Use the GCF to write 9+99 as a product.
  3. Use the GCF to write 30+21 as a product.
  4. Use the GCF to write 12+32 as a product.
  5. Use the GCF to write 40+55 as a product.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Greatest Common FactorAnswer keyVersion 1

Date Period

Find each greatest common factor, or solve each problem.

  1. Find the greatest common factor

    Find the GCF of 12 and 18.6
  2. Find the GCF of 8 and 10.2
  3. Find the GCF of 12 and 9.3
  4. Find the GCF of 24 and 20.4
  5. Find the GCF of 21 and 35.7
  1. Solve GCF word problems

    56 granola bars and 40 juice boxes are split into identical bags with none left over. What is the greatest number of bags?8 bags
  2. 35 red roses and 20 white roses are split into identical bags with none left over. What is the greatest number of bags?5 bags
  3. 6 bouncy balls and 9 stickers are split into identical bags with none left over. What is the greatest number of bags?3 bags
  4. 88 pencils and 55 erasers are split into identical bags with none left over. What is the greatest number of bags?11 bags
  5. 36 pencils and 84 erasers are split into identical bags with none left over. What is the greatest number of bags?12 bags
  1. Find the GCF of monomials

    Find the GCF of 7x3 and 14x.7x
  2. Find the GCF of 12a and 60a.12a
  3. Find the GCF of 48a2 and 8a3.8a2
  4. Find the GCF of 3m and 3m4.3m
  5. Find the GCF of 24x and 24x5.24x
  1. Use the GCF to factor a sum

    Use the GCF to write 5+25 as a product.5(1+5)
  2. Use the GCF to write 9+99 as a product.9(1+11)
  3. Use the GCF to write 30+21 as a product.3(10+7)
  4. Use the GCF to write 12+32 as a product.4(3+8)
  5. Use the GCF to write 40+55 as a product.5(8+11)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

The GCF of 24 and 36

  1. 24 is 2 x 2 x 2 x 3.
  2. 36 is 2 x 2 x 3 x 3.
  3. They share 2 x 2 x 3.

The answer is 12.

Where students go wrong

Stopping at a common factor rather than the greatest one. Four divides both 24 and 36, but so does 12, and only the largest counts.

Also called GCF, highest common factor, HCF or greatest common divisor.

What you can put on this worksheet

The greatest common factor
Find the GCF of 20 and 25. → 5
Word problems
30 pencils and 35 erasers are split into identical bags with none left over. What is the greatest number of bags? → 5 bags
The GCF of monomials
Find the GCF of 35x and 21x3. → 7x
Monomials with no variable in common
Find the GCF of 14y2, 16x3 → 2
Write a sum as a product
Use the GCF to write 28+36 as a product. → 4(7+9)

Questions about these worksheets

Yes. Every greatest common factor sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the greatest common factor questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: the greatest common factor, word problems, the gcf of monomials, monomials with no variable in common and write a sum as a product. Tick as many as you want and set how many of each, or let it spread them evenly.

Stopping at a common factor rather than the greatest one. Four divides both 24 and 36, but so does 12, and only the largest counts.