{
    "name": "Common Factor Calculator",
    "url": "https://calculators.geekmidst.com/calculators/common-factor-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/common-factor-calculator.md",
    "category": "Mathematics",
    "description": "List every factor that two or more whole numbers have in common, count them and find the greatest one.",
    "summary": "The common factors of a set of numbers are exactly the factors of their greatest common factor, so they are listed from the GCF’s divisors.",
    "also_called": [
        "Common divisors calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "numbers",
            "label": "Whole numbers",
            "type": "textarea",
            "default": "24, 36"
        }
    ],
    "outputs": [
        {
            "key": "common",
            "label": "Common factors",
            "format": "text"
        },
        {
            "key": "count",
            "label": "How many",
            "format": "integer"
        },
        {
            "key": "gcf",
            "label": "Greatest common factor",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "Common factors of a, b, … = the divisors of gcd(a, b, …)",
        "variables": {
            "gcd": "greatest common divisor"
        }
    },
    "worked_example": {
        "inputs": {
            "numbers": "24, 36"
        },
        "steps": [
            "gcd(24, 36) = 12.",
            "The divisors of 12 are 1, 2, 3, 4, 6 and 12.",
            "Each of these divides both 24 and 36, and no other number does."
        ],
        "result": "24 and 36 have six common factors: 1, 2, 3, 4, 6 and 12."
    },
    "interpretation": "Common factors tell you the ways a set of quantities can be split into equal groups with nothing left over, for example 24 and 36 items can both be packed in groups of 1, 2, 3, 4, 6 or 12.",
    "assumptions": [
        "Positive whole numbers up to 10¹²."
    ],
    "limitations": [],
    "rules": null,
    "faqs": [
        {
            "question": "Is 1 always a common factor?",
            "answer": "Yes. When 1 is the only one, the numbers are called coprime."
        },
        {
            "question": "How is this different from the GCF calculator?",
            "answer": "The GCF calculator gives only the largest shared factor with Euclid’s working; this lists all of them."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Greatest Common Factor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/greatest-common-factor-calculator"
        },
        {
            "name": "Factor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/factor-calculator"
        },
        {
            "name": "Least Common Multiple Calculator",
            "url": "https://calculators.geekmidst.com/calculators/least-common-multiple-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}