{
    "name": "Long Division Calculator",
    "url": "https://calculators.geekmidst.com/calculators/long-division-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/long-division-calculator.md",
    "category": "Mathematics",
    "description": "Divide whole numbers by long division, step by step, and get the quotient, remainder, mixed number and exact repeating decimal.",
    "summary": "Long division works through the dividend one digit at a time: bring down a digit, see how many times the divisor fits, subtract, and carry the remainder.",
    "also_called": [
        "Division with remainder 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": "dividend",
            "label": "Dividend (number being divided)",
            "type": "number",
            "default": "1000"
        },
        {
            "name": "divisor",
            "label": "Divisor",
            "type": "number",
            "default": "7"
        }
    ],
    "outputs": [
        {
            "key": "answer",
            "label": "Answer",
            "format": "text"
        },
        {
            "key": "quotient",
            "label": "Quotient",
            "format": "integer"
        },
        {
            "key": "remainder",
            "label": "Remainder",
            "format": "integer"
        },
        {
            "key": "mixed",
            "label": "As a mixed number",
            "format": "text"
        },
        {
            "key": "decimal",
            "label": "Exact decimal (repeating block in brackets)",
            "format": "text"
        }
    ],
    "formula": {
        "text": "Dividend = Divisor × Quotient + Remainder, with 0 ≤ Remainder < Divisor",
        "variables": {
            "Dividend": "the number being divided",
            "Divisor": "the number you divide by"
        }
    },
    "worked_example": {
        "inputs": {
            "dividend": "1000",
            "divisor": "7"
        },
        "steps": [
            "10 ÷ 7 = 1, remainder 3; bring down 0 to make 30.",
            "30 ÷ 7 = 4, remainder 2; bring down 0 to make 20.",
            "20 ÷ 7 = 2, remainder 6. Quotient 142, remainder 6; check: 7 × 142 + 6 = 1000."
        ],
        "result": "1000 ÷ 7 = 142 remainder 6, which is 142 6/7 or 142.857142857… with 857142 repeating."
    },
    "interpretation": "The remainder is what is left over after sharing out equally. Every fraction gives a decimal that either ends or repeats; the repeating block, shown in brackets, is written with a bar over it in many textbooks.",
    "assumptions": [
        "Whole-number dividend from 0 to 10¹⁵ and divisor from 1 to 10⁹."
    ],
    "limitations": [
        "Repeating blocks longer than 1,000 digits are cut off and marked."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "How do I check a long division?",
            "answer": "Multiply the quotient by the divisor and add the remainder. You should get the dividend back."
        },
        {
            "question": "Why does 1/7 repeat with six digits?",
            "answer": "There are only six possible non-zero remainders when dividing by 7, so the remainders, and therefore the digits, must start repeating within six steps."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Fraction Calculator",
            "url": "https://calculators.geekmidst.com/calculators/fraction-calculator"
        },
        {
            "name": "Rounding Calculator",
            "url": "https://calculators.geekmidst.com/calculators/rounding-calculator"
        },
        {
            "name": "Big Number Calculator",
            "url": "https://calculators.geekmidst.com/calculators/big-number-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}