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.
What This Calculator Does & Who It's For
Calculator Purpose & Ideal Users
- 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 โHow it was calculatedโ).
- Ideal Users:Students & homework: โList all common factors of 12 and 18,โ โfind the GCF of 3 numbers.โ 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 fractionsโfor 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.
This common factor calculator finds the GCF and every common factor (shared divisor) of two or more positive integers.
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 evenlyโthe 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, โฆ So factors โgo intoโ the number; multiples are โwhat you get when you multiply.โ This calculator deals with factors (divisors) and finds which ones are common across all your numbersโideal 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. โFactorโ and โdivisorโ 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 solverโit 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 โn), then take the intersection of those sets. To find the greatest common factor only: use the Euclidean algorithmโGCD(a, b) = GCD(b, a mod b)โand 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 โHow it was calculatedโ 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 solverโenter 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.