Long Division Calculator
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What Your Result Means
- Quotient: The whole number of times the divisor fits into the dividend. This is the integer part of the division result.
- Remainder: What is left over after the divisor has been subtracted as many whole times as possible. A remainder of 0 means the division is exact.
- Decimal Result: The quotient expressed as a decimal number, showing the fractional part that the remainder represents.
- Mixed Number: The result written as a whole number plus a proper fraction (reduced to lowest terms), which is the standard way to express division results in arithmetic.
How This Calculator Works
You enter an integer dividend and a nonzero integer divisor. The tool computes the whole-number quotient using floor division, the integer remainder using the modulo operation, and the decimal result by standard division. It also reduces the remainder over the divisor to lowest terms using the greatest common divisor to produce the mixed number form. The step-by-step work walks through the standard long division algorithm digit by digit.
Quick Questions
What happens if the divisor is larger than the dividend?
The quotient will be 0 and the remainder equals the dividend. The result is shown as a proper fraction (e.g., 3 ÷ 7 = 0 remainder 3, or 3/7 as a fraction).
Can I divide negative numbers?
Yes. The calculator handles negative dividends and divisors. Note that conventions for the sign of the remainder can vary across programming languages and math textbooks.
Why does the decimal result sometimes show many digits?
Some divisions produce repeating decimals (like 1 ÷ 3 = 0.333...). The calculator shows up to 10 decimal places to give you a precise approximation without displaying infinitely many digits.
How is the mixed number simplified?
The tool finds the greatest common divisor (GCD) of the remainder and divisor, then divides both by it. For example, 6/8 is reduced to 3/4 because GCD(6, 8) = 2.
Is this the same as the long division taught in school?
Yes. The step-by-step work mirrors the standard algorithm: bring down each digit of the dividend, divide by the divisor, record the quotient digit, and carry the remainder to the next step.
Sources
- Wikipedia — Long Division (standard algorithm and notation)
- Wikipedia — Euclidean Division (formal definition of quotient and remainder)
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.