Factors & Multiples Worksheet Generator (GCF and LCM)
Make a printable factors and multiples worksheet in seconds: list factors, write multiples, find the greatest common factor and least common multiple, break numbers into prime factors and solve GCF and LCM word problems. Three levels, with an answer key.
Choose one skill or a mixed sheet, pick a level and print. Easy uses numbers up to 36; Standard up to 72; Challenge up to 180, with some three-number GCFs and LCMs and prime factorizations written with exponents.
Numbers up to 72, the first 6 multiples, GCFs up to 12, LCMs up to 180.
PDF puts the answer key on its own page.
Factors & Multiples
12 problems · Mixed (factors, multiples, GCF, LCM) · Standard
Name: ______________________ Date: ____________
List all the factors of each number.
58:
56:
50:
Write the first 6 multiples of each number.
15:
9:
14:
Find the greatest common factor (GCF).
GCF(20, 58) =
GCF(35, 42) =
GCF(30, 72) =
Find the least common multiple (LCM).
LCM(12, 20) =
LCM(16, 20) =
LCM(10, 12) =
Answer key
List all the factors of each number.
58: 1, 2, 29, 58
56: 1, 2, 4, 7, 8, 14, 28, 56
50: 1, 2, 5, 10, 25, 50
Write the first 6 multiples of each number.
15: 15, 30, 45, 60, 75, 90
9: 9, 18, 27, 36, 45, 54
14: 14, 28, 42, 56, 70, 84
Find the greatest common factor (GCF).
GCF(20, 58) = 2
GCF(35, 42) = 7
GCF(30, 72) = 6
Find the least common multiple (LCM).
LCM(12, 20) = 60
LCM(16, 20) = 80
LCM(10, 12) = 60
Answer Key · Factors & Multiples
12 problems · Mixed (factors, multiples, GCF, LCM) · Standard
List all the factors of each number.
58: 1, 2, 29, 58
56: 1, 2, 4, 7, 8, 14, 28, 56
50: 1, 2, 5, 10, 25, 50
Write the first 6 multiples of each number.
15: 15, 30, 45, 60, 75, 90
9: 9, 18, 27, 36, 45, 54
14: 14, 28, 42, 56, 70, 84
Find the greatest common factor (GCF).
GCF(20, 58) = 2
GCF(35, 42) = 7
GCF(30, 72) = 6
Find the least common multiple (LCM).
LCM(12, 20) = 60
LCM(16, 20) = 80
LCM(10, 12) = 60
What is the difference between factors and multiples?
A factor of a number divides it with no remainder: the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is the number times 1, 2, 3 and so on: the multiples of 12 are 12, 24, 36…
The greatest common factor (GCF) of two numbers is the largest factor they share: GCF(12, 18) = 6. The least common multiple (LCM) is the smallest multiple they share: LCM(4, 6) = 12. GCF problems usually share things into equal groups; LCM problems ask when repeating events happen together.
How to use the factors & multiples worksheet generator
- 1Choose the practice: factors, multiples, GCF, LCM, GCF and LCM together, prime factorization, word problems, or mixed.
- 2Pick a level; the note under the menus gives its number ranges.
- 3Choose 8, 12 or 16 problems and whether to include the answer key.
- 4Press Regenerate worksheet for different numbers, then print or download the PDF.
When this is useful
Factor fluency
Listing every factor in pairs (1 × 24, 2 × 12, 3 × 8, 4 × 6) builds the number sense GCF and fractions depend on.
Simplifying fractions
GCF practice is the step before simplifying fractions; LCM practice before adding fractions with unlike denominators.
Prime factorization
Break numbers into primes, written out (2 × 2 × 3) or, at Challenge, with exponents (2² × 3).
Choosing the right tool
Word problems mix GCF and LCM situations, so students first decide which one the question needs.
Examples to try
Factors
24: 1, 2, 3, 4, 6, 8, 12, 24.
GCF and LCM
GCF(18, 30) = 6; LCM(6, 8) = 24.
Three numbers, Challenge
GCF(24, 36, 60) = 12; LCM(4, 6, 9) = 36.
Prime factorization
60 = 2 × 2 × 3 × 5, or 2² × 3 × 5 at Challenge.
Word problem
Buses every 6 and 8 minutes leave together at 8:00. They next leave together after LCM(6, 8) = 24 minutes.
Tips for better results
Find factors in pairs
Stop when the pairs meet. Students who list factors one by one often miss the large ones.
Check that the LCM is a multiple of both
And that the GCF divides both. A quick check catches most slips.
Ask "sharing or meeting again?"
Equal groups with nothing left over is GCF; events repeating until they coincide is LCM.
Avoid the trivial case
The generator rarely gives pairs where one number is a multiple of the other, so the LCM isn't simply the larger number.
How the factors & multiples worksheet generator works
Every answer is computed exactly and checked by unit tests against a brute-force search. GCF problems are built from a shared factor, so the GCF is always greater than 1; LCM problems mostly avoid pairs where the larger number is already the answer.
Each sheet comes from a seed, so the same settings always give the same sheet, and Regenerate worksheet gives a different one.
Private by design
- No account and no sign-up. Just open it and start.
- Everything runs on your device, which keeps your settings private.
- Nothing you create is uploaded. No values, names, scores, or generated content are sent to our servers. If you're signed in, My Classeem's Recent Activity notes which tools you used — never what you did in them.
- We use Google Analytics for anonymous, aggregate measurement: page views and a few usage events, such as a worksheet being printed or a game round starting or finishing (with the mode played). It never receives what you enter — no answers, scores, names, or generated content.
Frequently asked questions
What grade is this for?
Factors and multiples are usually introduced in grade 4; GCF, LCM and prime factorization in grades 5 and 6.
Is 1 counted as a factor?
Yes. Every list of factors starts with 1 and ends with the number itself.
Are the word problems always GCF or LCM?
Yes: each is one of two GCF situations (equal kits, square plots) or two LCM situations (buses, blinking lights), mixed so students decide which to use.
Can I get three-number GCF and LCM problems?
Yes, some appear at the Challenge level.
Is there an answer key?
Yes, on its own page, with full factor lists and prime factorizations.
More classroom tools
Exponents Worksheet Generator
Printable exponent practice: find the value of powers, write products as powers, find missing exponents and use the exponent laws.
Equivalent Fractions Worksheet Generator
Make printable equivalent fractions practice with a missing numerator or denominator, plus an answer key.
Division Worksheet Generator
Make printable division worksheets, from 0-12 facts to long division, with or without remainders and a matching answer key.
Always free · No account needed · Nothing you type leaves your device unless you choose to save it.