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  4. Common Factor Calculator

Common Factor Calculator

List every positive factor shared by two or more integers, with per-number factor lists and the GCF.

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How it works

Common factors are positive integers that divide every input. They are exactly the positive divisors of the GCF of the list; the GCF itself is the largest common factor.

common factors = divisors(gcd(…))

When to use

Use this tool when you need to: try 330, 75, 450, 225 → 1, 3, 5, 15 (GCF 15), or 16, 12 → 1, 2, 4. Related: GCF and Factor calculators.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Try 330, 75, 450, 225 → 1, 3, 5, 15 (GCF 15), or 16, 12 → 1, 2, 4. Related: GCF and Factor calculators.

Frequently asked questions

What is the Common Factor Calculator?
Common factors are positive integers that divide every input. They are exactly the positive divisors of the GCF of the list; the GCF itself is the largest common factor.
How do I use the Common Factor Calculator?
Enter the required values, then calculate. The Common Factor Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Common Factor Calculator use?
common factors = divisors(gcd(…))

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Common factor calculator

Enter two or more non-zero integers separated by commas. See every positive factor they share, each input’s full factor list, and the GCF.

Separate integers with commas (or spaces). Negatives use absolute values. Zero is not allowed.

Try an example

How it works

What is a factor?

A factor is a term in multiplication. For example, in 3 × 4 = 12, both 3 and 4 are factors of 12. A number can have several factor pairs: 3 × 4 = 12 2 × 6 = 12 1 × 12 = 12 So 1, 2, 3, 4, 6, and 12 are all factors of 12. This tool is about positive integer factors (not algebraic factoring of expressions).

What is a common factor?

A common factor (also called a common divisor) is a positive integer shared by every number you enter. Example — factors of 16: 1, 2, 4, 8, 16. Factors of 12: 1, 2, 3, 4, 6, 12. Common factors of 16 and 12: 1, 2, and 4. The greatest common factor in that case is 4. Problems often ask for the GCF alone; this calculator lists every shared factor, then highlights the GCF as the largest one. You can use two numbers or more — for example GCF and common factors of 330, 75, 450, and 225.

How common factors are found

Two equivalent approaches: 1. List the positive factors of each number and take the intersection of those sets (clear for small values). 2. Compute the GCF of the list, then list every positive divisor of that GCF. Those divisors are exactly the common factors — efficient for longer lists or larger numbers. Example: GCF(330, 75, 450, 225) = 15, whose factors 1, 3, 5, 15 are the common factors of all four numbers.

Related calculators

GCF focuses on the single greatest shared divisor; Factor lists every divisor of one number; LCM finds the least shared multiple.

  • Greatest Common Factor Calculator
  • Factor Calculator
  • Least Common Multiple Calculator
  • Prime Factorization Calculator