Long Division Calculator
Quotient, Remainder & Step-by-Step Work
Mastering Long Division
Long division breaks a large division problem into a sequence of small, manageable steps — bring down a digit, divide, multiply, subtract, and repeat — making it possible to divide numbers of any size by hand.
Every step of a long division problem follows the same pattern: divide, multiply, subtract, and bring down the next digit. Our work grid lays out each of these steps exactly as you'd write them on paper.
Stopping at a whole-number remainder is useful for problems like splitting items evenly, while continuing into decimal places gives you a precise decimal answer for problems that need more granularity.
The Four-Step Cycle
Long division repeats the same four-step cycle for every digit: Divide the divisor into the current value, Multiply the divisor by that quotient digit, Subtract the product from the current value, and Bring down the next digit to form the next value. This is sometimes remembered with the mnemonic "Does McDonald's Sell Burgers?"
Key Takeaways
- The remainder is always smaller than the divisor. If it isn't, the division wasn't carried far enough.
- Decimal continuation appends zeros after the decimal point and keeps dividing, turning a leftover remainder into precise decimal digits.
- The sign of the result depends on both numbers. A negative result comes from dividing exactly one negative value by one positive value.
Frequently Asked Questions
- Enter the dividend (the number being divided) and the divisor (the number you're dividing by).
- Click "Calculate" to see the quotient and remainder, along with the full bring-down work grid.
- Turn on "Continue into decimal places" if you want the division to keep going past the remainder into decimal digits instead of stopping there.
The quotient is the whole-number result of the division — how many whole times the divisor fits into the dividend. The remainder is whatever is left over after subtracting out all those whole divisions. For example, dividing 17 by 5 gives a quotient of 3 (since 5 fits into 17 three whole times) with a remainder of 2 (since 3 × 5 = 15, leaving 17 − 15 = 2).
Long division works one digit at a time: at each step, the next digit of the dividend is "brought down" next to whatever remainder is left over, the divisor is subtracted out as many whole times as possible, and the process repeats with the new remainder. The work grid shows every one of these steps — the value being divided, the amount subtracted, and the remainder carried into the next step — exactly like the long division you'd write out by hand.
By default, the calculator stops once it reaches the end of the dividend's digits and reports whatever is left over as the remainder. Turning on decimal continuation instead keeps the bring-down process going by appending zeros after a decimal point, producing a decimal answer (like 2.5 instead of "quotient 2, remainder 1") to the number of decimal places you choose.
Yes. The calculator determines the sign of the result from the signs of the dividend and divisor (a result is negative when exactly one of the two is negative), performs the long division on the absolute values, and then applies the correct sign to the quotient, remainder, and decimal result.
Division by zero is mathematically undefined, so the calculator shows a clear error instead of attempting the calculation. Long division as taught in school also assumes whole-number inputs, so the dividend and divisor must both be whole numbers — use decimal continuation to get a decimal-valued answer instead.