Free Long Division Calculator
Work out the quotient and remainder for any two numbers instantly, with a full step-by-step breakdown showing exactly how the answer is reached — just like doing it by hand.
Understanding Long Division
Long division is the process of breaking a large division problem into a series of smaller, manageable steps. Even when numbers don’t divide evenly, long division lets you find exactly how many times one number fits into another, plus what’s left over.
Key Terms You Need
The building blocks of every division problem
The Dividend
The dividend is the number being divided up — the total amount you’re starting with, and the number written first in the division problem.
The Divisor
The divisor is the number you are dividing by — it tells you how many equal groups you are trying to split the dividend into.
The Quotient
The quotient is the whole-number result of the division — how many times the divisor fits completely into the dividend.
The Remainder
If the dividend doesn’t divide evenly, whatever is left over after the last full subtraction is called the remainder, and it’s always smaller than the divisor.
Long Division Calculator
Enter a dividend and divisor to see the full solution
How to Do Long Division
Follow these four steps to solve any long division problem by hand, or simply enter your numbers into the calculator above for an instant, fully worked solution.
Set Up the Problem
Write the dividend inside the division bracket and the divisor outside it. Work from the leftmost digit of the dividend, taking just enough digits to form a number at least as large as the divisor.
Divide and Multiply
Work out how many whole times the divisor fits into that portion of the dividend, write that digit above, then multiply it by the divisor to see how much you’ve accounted for.
Subtract and Bring Down
Subtract the multiplication result from the current portion of the dividend, then bring down the next digit of the dividend to continue the process.
Repeat Until Every Digit Is Used
Keep dividing, multiplying, subtracting, and bringing down digits until you’ve used every digit of the dividend. Whatever remains after the final subtraction is the remainder.
Exact vs Division With Remainder
A side-by-side summary of how division behaves depending on whether the dividend splits evenly by the divisor.
| Feature | Exact Division | Division With Remainder |
|---|---|---|
| Definition | The dividend splits perfectly into equal whole groups. | Some amount is left over after dividing into whole groups. |
| Remainder value | Always zero. | A whole number smaller than the divisor. |
| Result type | A whole-number quotient only. | A quotient plus a remainder, or a decimal quotient. |
| Example | 36 ÷ 6 = 6, remainder 0. | 37 ÷ 6 = 6, remainder 1. |
| Continuing further | No further steps needed. | Can be extended into decimals by adding zeroes. |
| Which is more common? | Most real-world division problems produce a remainder rather than dividing exactly. | |
Long Division FAQ
Answers to the most frequently asked questions about long division, quotients, and remainders.
Long division is a step-by-step method for dividing one number (the dividend) by another (the divisor) by working through the digits one at a time to find a quotient and, if the numbers don’t divide evenly, a remainder.
The dividend is the number being divided, the divisor is the number you are dividing by, the quotient is the whole-number result of the division, and the remainder is whatever is left over if the division doesn’t divide evenly.
Divide the divisor into the leftmost digits of the dividend, multiply the divisor by that result, subtract to find the remainder, bring down the next digit, and repeat the process until every digit has been used.
If the dividend is not exactly divisible by the divisor, the final subtraction leaves a non-zero remainder, which can either be left as a whole-number remainder or continued as a decimal by adding zeroes and carrying on the division.
Yes. Long division can be extended to decimals by continuing to bring down zeroes after the decimal point, allowing you to calculate the quotient to as many decimal places as needed.