When You Need the GCF Only
Use when you only need the single number (e.g. simplifying fractions, coprime check), results panel shows it first.
Modular arithmetic & digits
Common Factor Calculator
Find the GCF and all common factors of two or more integers. Common divisor solver with prime factorization.
By Jeff Beem
Updated
Numbers
Positive integers only (1 or more numbers). Non-numeric characters are ignored. No limit on how many numbers, enter as many as you need.
Result
Greatest Common Factor (GCF)6
All common factors (4)
1, 2, 3, 6
Individual factor breakdown
| Number | Divisors |
|---|---|
| 12 | 1, 2, 3, 4, 6, 12 |
| 18 | 1, 2, 3, 6, 9, 18 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
How it was calculated
Prime factorization for each number. The GCF is the product of the lowest power of all common prime bases.
- 12=2^2 × 3
- 18=2 × 3^2
- 24=2^3 × 3
Using this calculator
The results panel shows the GCF and the full list of common factors in ascending order. Use the table for each number’s divisors and the “How it was calculated” section for prime factorizations. For what a factor is, factor vs. multiple, GCF vs. GCD, and how to find common factors by hand, see the article below.
When and How to Use the Common Factor Calculator
When to use which output, definitions and methods are in the article below.
Workflow Tips
When You Need All Common Factors
Use when homework or curriculum asks for the full list, not just the GCF.
When You Need the Breakdown
Use the factor table and "How it was calculated" for showing your work.
Copy for Reports or Homework
Use “Copy common factors” to paste the list elsewhere.
Common Factor Calculator: GCF & All Common Divisors
Free common factor calculator: find the greatest common factor (GCF) and all common factors of two or more numbers. Greatest common factor of 3 numbers, how to find all common factors, GCF vs GCD calculator, common divisor solver, common factors of 12 and 18.
How the Math Works
The Greatest Common Factor (GCF) of two or more integers is the largest positive integer that divides each of them with no remainder. This calculator finds the GCF using the Euclidean algorithm, which works by repeatedly replacing the larger number with the remainder of dividing the two: GCF(a, b) becomes GCF(b, a mod b) until the remainder reaches zero. For three or more numbers, the algorithm chains: GCF(a, b, c) = GCF(a, GCF(b, c)). For example, GCF(24, 36) proceeds as 36 mod 24 = 12, then 24 mod 12 = 0, so the GCF is 12. The calculator also lists every common factor by computing divisors of each number and taking their intersection. Prime factorization provides an alternative method: decompose each number into primes, then multiply the lowest power of each shared prime. For 24 = 2³ × 3 and 36 = 2² × 3², the GCF is 2² × 3 = 12.
- Euclidean Algorithm:GCF(a, b) = GCF(b, a mod b), repeated until remainder = 0
- Multiple Numbers:GCF(a, b, c) = GCF(a, GCF(b, c))
- Prime Factorization:Take the lowest power of each shared prime and multiply
How to Use This Calculator
Type two or more positive integers separated by commas into the input field (for example, 12, 18 or 24, 36, 60). The calculator displays the Greatest Common Factor at the top of the results panel, followed by every common factor in ascending order. Below that, the individual factor table lists all divisors for each number you entered, making side-by-side comparison straightforward. Use the Copy common factors button to paste the full list into homework, a report, or another application. Expand the How it was calculated section to see the prime factorization of each number and the step-by-step derivation of the GCF. Non-numeric entries are ignored, and results update as you type.
What This Calculator Does & Who It's For
Calculator Purpose & Ideal Users
This common factor calculator finds the GCF and every common factor (shared divisor) of two or more positive integers.
- What You'll Get:GCF: The largest number that divides all your numbers. All common factors: The full list of shared divisors in ascending order. Individual factor table: Divisors for each number you entered. Prime factorizations: Step-by-step breakdown for each number (in “How it was calculated”).
- Ideal Users:Students & homework: “List all common factors of 12 and 18,” “find the GCF of 3 numbers.” Teachers & curriculum: Quick checks, worksheets, and number-theory examples. Anyone simplifying fractions or scaling: GCF for reducing ratios or scaling recipes. Coprime checks: See if the only common factor is 1.
- Scope & Limits:Positive integers only; non-numeric input is ignored. No decimals or fractions, for those, use a ratio or fraction tool. The calculator uses the Euclidean algorithm for the GCF and set intersection for all common factors; results update as you type.
What Is a Common Factor Calculator? GCF and Common Divisor Solver
A common factor calculator (or GCF calculator, common divisor solver) finds the Greatest Common Factor (GCF) and all shared divisors of two or more positive integers from a comma-separated list. Use it for greatest common factor of 3 numbers or more, how to find all common factors, or a GCF vs GCD calculator (they are the same). See above for what you'll get and who it's for. Free online, no sign-up.
Factor vs. Multiple: What Is a Factor?
A factor of an integer is a divisor that divides it evenly, the result is a whole number with no remainder. For example, common factors of 12 and 18 are the divisors shared by both: 1, 2, 3, and 6; the GCF of 12 and 18 is 6. A multiple of an integer is the product of that number and another integer: multiples of 4 are 4, 8, 12, 16, … So factors “go into” the number; multiples are “what you get when you multiply.” This calculator deals with factors (divisors) and finds which ones are common across all your numbers, ideal when you need to find common factors of two numbers or list all common factors for homework or curriculum.
The GCF / GCD Distinction: GCF vs GCD Calculator
Greatest Common Factor (GCF) and Greatest Common Divisor (GCD) are mathematically identical: the largest positive integer that divides all given numbers with no remainder. “Factor” and “divisor” are used interchangeably. Whether you search for a GCF calculator or a GCD calculator, you get the same result. This tool is a common factor calculator and common divisor solver, it gives you the GCF (or GCD) plus the complete list of common factors.
How to Find Common Factors Manually: List Divisors and Intersect
To find all common factors: list the positive divisors of each number (from 1 up to the number, or use pairs from 1 to √n), then take the intersection of those sets. To find the greatest common factor only: use the Euclidean algorithm, GCD(a, b) = GCD(b, a mod b), and for greatest common factor of 3 numbers, apply it in sequence: GCF(a, b, c) = GCF(a, GCF(b, c)). Alternatively, use prime factorization and take the lowest power of each common prime; the product is the GCF. This calculator does all of that and shows the prime factorization for each number in the “How it was calculated” section.
Common Factor Calculator FAQ
What is the common factor of 12 and 18?
The common factors of 12 and 18 are the numbers that divide both evenly: 1, 2, 3, and 6. The Greatest Common Factor (GCF) of 12 and 18 is 6. You can find them by listing divisors of each number and taking the intersection, or use this common factor calculator: enter "12, 18" to see all common factors and the GCF.
Can a common factor be a decimal?
No. In standard number theory, factors and common factors are defined for integers only. A factor must divide the number evenly with no remainder, so we work with whole numbers. This calculator finds common factors and the GCF for positive integers only; for decimals or fractions you would use a different tool (e.g. simplifying ratios).
Is 1 always a common factor?
Yes. 1 divides every integer evenly, so whenever you have two or more positive integers, 1 is always a common factor. The GCF is at least 1; if the only common factor is 1, we say the numbers are coprime (or relatively prime). This calculator always lists 1 in the common factors when you enter at least one number.
What is the difference between GCF and GCD?
GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are the same thing: the largest positive integer that divides all given numbers with no remainder. "Factor" and "divisor" are used interchangeably here. This common factor calculator is a GCF calculator and a common divisor solver, enter your numbers to get the GCF and the full list of common factors.
How do I find the greatest common factor of 3 numbers?
Use the same idea as for two numbers: list all common factors by finding divisors of each number and taking the intersection, or use the Euclidean algorithm repeatedly: GCF(a, b, c) = GCF(a, GCF(b, c)). This calculator accepts a comma-separated list (e.g. 24, 36, 60) and shows the GCF, all common factors, and prime factorizations for each number.
Mathematical Reference Note
Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.
Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.
Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.
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