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Long Division Calculator — Quotient & Remainder

Enter a dividend and divisor to get the quotient, remainder, and full decimal result, along with a step to verify the answer.

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📝 Enter Dividend and Divisor

📊 Result

Enter a dividend and divisor to divide
⚠️

Disclaimer: This tool performs standard mathematical calculations for educational and reference purposes. Always double-check results independently for graded coursework or exams.

How Long Division Works

Long division breaks a division problem into two whole-number pieces: a quotient (how many times the divisor fits into the dividend) and a remainder (whatever is left over after the divisor has been subtracted as many whole times as possible). Together they can always be checked with one relationship: dividend = divisor × quotient + remainder.

Handling Negative Numbers

This calculator always reports the remainder as zero or positive, matching the convention taught in classroom long division, even when the dividend or divisor is negative. Some programming languages return a negative remainder when the dividend is negative, but that's a technical detail of how their modulo operator is built, not the mathematical definition used here. The quotient is adjusted so the check equation, dividend = divisor × quotient + remainder, always holds true.

Worked Example

Divide 47 by 5.

  1. Step 1: 5 fits into 47 a total of 9 whole times, since 5 × 9 = 45
  2. Step 2: Subtract: 47 − 45 = 2, which is the remainder
  3. Step 3: As a full decimal, 47 ÷ 5 = 9.4
  4. Step 4: Check: 5 × 9 + 2 = 47 ✓

Frequently Asked Questions

This calculator follows the standard long-division convention where the remainder must always be zero or positive and smaller than the divisor's absolute value. Some programming languages return a negative remainder for negative dividends, but that's a quirk of how the % operator is implemented, not the mathematical definition used in classroom long division.
Multiply the divisor by the quotient, then add the remainder — the result should always equal the original dividend. This calculator shows that verification line automatically so you can confirm the answer at a glance instead of re-doing the arithmetic by hand.
Division by zero is undefined in ordinary arithmetic, so the calculator blocks it and asks for a non-zero divisor instead of returning an error code or an infinite value.
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