Divide numbers and see the working. This free long division calculator gives the quotient, remainder, decimal and mixed-number answers, with each step (divide, multiply, subtract, bring down) laid out.
Enter whole numbers to see the quotient and remainder, the decimal answer, and the full long-division working laid out step by step.
Long division breaks the problem into repeated steps: divide, multiply, subtract, bring down the next digit. The working below mirrors how it’s done by hand.
How the Long Division Calculator Works
Long division splits one whole number by another into a quotient and a remainder, then shows the same answer as a decimal or a mixed number. This calculator does the arithmetic and also lays out the divide-multiply-subtract-bring-down steps you’d use to solve it by hand.
Formula: Quotient = floor(Dividend ÷ Divisor), and Remainder = Dividend − (Quotient × Divisor). The decimal answer is simply Dividend ÷ Divisor. The mixed-number form is Quotient, Remainder/Divisor, with the remainder and divisor both divided by their greatest common factor (GCF) to simplify the fraction.
- Dividend — the number being divided (entered at the top)
- Divisor — the number you’re dividing by
- Quotient — the whole-number result of the division, shown as the main answer
- Remainder — what’s left over after the divisor no longer fits evenly
Example Scenarios
| Dividend | Divisor | Quotient | Remainder | Decimal Answer |
|---|---|---|---|---|
| 1,234 | 7 | 176 | 2 | 176.285714 |
| 100 | 8 | 12 | 4 | 12.5 |
| 50 | 5 | 10 | 0 | 10 (exact) |
| 29 | 4 | 7 | 1 | 7.25 |
| 17 | 3 | 5 | 2 | 5.666667 |
Long Division Calculator FAQ
What’s the difference between the quotient and the remainder?
The quotient is how many whole times the divisor fits into the dividend. The remainder is whatever amount is left over that doesn’t divide evenly — it’s always smaller than the divisor. Together, quotient × divisor + remainder always equals the original dividend.How do I turn a remainder into a decimal answer?
Divide the remainder by the divisor and add that to the quotient, or simply divide the dividend by the divisor directly. For example, 29 ÷ 4 gives quotient 7 and remainder 1, and 1 ÷ 4 = 0.25, so the decimal answer is 7.25.What does the “mixed number” result actually show?
It expresses the answer as a whole number plus a fraction, using the remainder over the divisor, simplified by their greatest common factor. For 29 ÷ 4, that’s 7 and 1/4, which is the same value as the decimal 7.25 written differently.Can this calculator divide negative numbers?
Yes. It divides the absolute values first to get the quotient and remainder, then applies a negative sign to the result if the dividend and divisor have opposite signs, matching standard mathematical convention for signed division.Why does long division involve “bringing down” digits?
Long division processes the dividend one digit at a time because dividing the whole number at once is impractical by hand. Each step brings the next digit down, attaches it to the running remainder, and figures out how many times the divisor fits before repeating.What happens if I divide by zero or divide a smaller number by a larger one?
Dividing by zero is undefined and the calculator won’t produce a result. Dividing a smaller dividend by a larger divisor is valid — you’ll simply get a quotient of 0 and a remainder equal to the original dividend.Related Calculators
A remainder from long division is really just a fraction waiting to be simplified — feed it into the fraction simplifier or the general-purpose fraction calculator to work with it further, and use the GCF calculator to see exactly how a mixed number gets reduced to lowest terms.