{
    "name": "Factor Calculator",
    "url": "https://calculators.geekmidst.com/calculators/factor-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/factor-calculator.md",
    "category": "Mathematics",
    "description": "List all the factors and factor pairs of a whole number, with the count, the sum and whether it is prime, perfect, abundant or deficient.",
    "summary": "A factor of n is a whole number that divides n with no remainder. Factors come in pairs that multiply to n, so only numbers up to √n need checking.",
    "also_called": [
        "Divisor calculator",
        "Factor pairs 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": "n",
            "label": "Whole number",
            "type": "number",
            "default": "36"
        }
    ],
    "outputs": [
        {
            "key": "factors",
            "label": "Factors",
            "format": "text"
        },
        {
            "key": "pairs",
            "label": "Factor pairs",
            "format": "text"
        },
        {
            "key": "count",
            "label": "Number of factors",
            "format": "integer"
        },
        {
            "key": "sum",
            "label": "Sum of factors",
            "format": "integer"
        },
        {
            "key": "prime_factors",
            "label": "Prime factorisation",
            "format": "text"
        },
        {
            "key": "classification",
            "label": "Type of number",
            "format": "text"
        }
    ],
    "formula": {
        "text": "If n = p₁^e₁ × p₂^e₂ × …, the number of factors is (e₁ + 1)(e₂ + 1)…, and every factor is p₁^k₁ × p₂^k₂ × … with 0 ≤ kᵢ ≤ eᵢ",
        "variables": {
            "pᵢ": "the distinct primes dividing n",
            "eᵢ": "their exponents"
        }
    },
    "worked_example": {
        "inputs": {
            "n": "36"
        },
        "steps": [
            "36 = 2² × 3², so it has (2 + 1)(2 + 1) = 9 factors.",
            "Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.",
            "Sum: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91."
        ],
        "result": "36 has nine factors, 1, 2, 3, 4, 6, 9, 12, 18 and 36, which add up to 91."
    },
    "interpretation": "A number with exactly two factors is prime. Square numbers have an odd number of factors because one pair repeats. Perfect numbers, such as 6 and 28, equal the sum of their factors other than themselves.",
    "assumptions": [
        "Positive factors only; each negative factor is just the negative of a positive one."
    ],
    "limitations": [
        "Numbers up to 10¹²."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Is 1 a prime number?",
            "answer": "No. A prime has exactly two factors, and 1 has only one."
        },
        {
            "question": "What is the difference between factors and multiples?",
            "answer": "Factors divide into the number (factors of 12 are 1, 2, 3, 4, 6, 12); multiples are the number times a whole number (12, 24, 36, …)."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Prime Factorization Calculator",
            "url": "https://calculators.geekmidst.com/calculators/prime-factorization-calculator"
        },
        {
            "name": "Common Factor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/common-factor-calculator"
        },
        {
            "name": "Greatest Common Factor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/greatest-common-factor-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}