This greatest common factor calculator finds the largest whole number that divides 2 or more integers exactly. It is based on standard GCF and Euclidean algorithm methods used in arithmetic and number theory. For a trusted educational reference this tool is based on, see Khan Academy’s explanation of the Euclidean algorithm: official reference.
What this calculator does
Enter whole numbers separated by commas, and the tool will calculate the greatest common factor, show the absolute values used, and break down the result step by step. It can also show prime factorization and Euclidean algorithm steps for a clearer explanation.
- Finds the greatest common factor for 2 or more whole numbers
- Handles negative numbers by using their absolute values for the GCF
- Handles zero correctly as long as at least one other number is non-zero
- Shows prime factorization steps when enabled
- Shows Euclidean algorithm steps when enabled
- Checks divisibility so you can confirm the result quickly
How to use it
- Enter at least 2 whole numbers separated by commas.
- Choose whether to show prime factorization and Euclidean algorithm steps.
- Click Calculate.
- Read the GCF, the breakdown, and the divisibility check below.
What the result means
The greatest common factor is the largest positive whole number that divides every entered number evenly. If the GCF is 12, that means each number can be divided by 12 with no remainder. This is useful for simplifying ratios, reducing fractions, factoring expressions, and solving many basic algebra problems.
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