What this calculator does
Long division is the method for dividing one whole number by another by hand, one digit at a time, rather than in a single leap. This long division calculator carries out the same method a person would use on paper: bring down the next digit of the dividend, work out how many times the divisor fits, subtract that product, and carry the remainder into the next step.
The result is the same quotient and remainder a calculator’s divide key gives you, but with the working shown, which is the part most division tools skip. That working is what actually needs checking when a division problem is being learned or marked, not just the final answer.
The formula
Starting from the leftmost digit of the dividend, bring down one digit at a time to build a running value. At each step, divide that running value by the divisor, write down how many times it fits (a digit of the quotient), subtract the product of that digit and the divisor, and carry the remainder forward to combine with the next digit brought down. The process ends when every digit of the dividend has been brought down; whatever is left over is the final remainder.
| Term | Meaning |
|---|---|
| Dividend | The number being divided. |
| Divisor | The number the dividend is divided by. |
| Quotient | The whole-number result of the division, built up one digit at a time. |
| Remainder | Whatever is left over once the divisor no longer fits evenly into what remains. |
The inputs explained
| Field | What to enter |
|---|---|
| Dividend (the number being divided) | The whole number being divided, entered as a non-negative integer. |
| Divisor (the number dividing it) | The whole number to divide by, entered as an integer greater than zero. |
When to use it
Checking homework working
Rather than only confirming the final quotient and remainder, the step-by-step table shows exactly where a bring-down or subtraction step went wrong, which is usually more useful than the answer alone.
Dividing without a calculator to hand
For a dividend too large to divide mentally, working through it one digit at a time, the way this calculator lays out, is the standard fallback method.
Understanding where a remainder comes from
Seeing each subtraction step makes it clear why a division does not always come out even, and exactly how much is left over and at which step it appeared.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the quotient and remainder change as the dividend grows, at a fixed divisor
A fixed divisor of 7, against a range of dividends.
How the quotient and remainder change with the divisor, at a fixed dividend
A fixed dividend of 1,000, against a range of divisors.
Questions
What is the difference between long division and short division?
Short division carries the remainder mentally between digits and writes only the final quotient. Long division writes out the subtraction at every step, which is easier to follow and check for larger numbers or bigger divisors.
Why is the remainder always smaller than the divisor?
If what is left over were equal to or larger than the divisor, the divisor would fit at least one more time, and that extra fit would already have been counted in the quotient at that step.
Can this handle a dividend smaller than the divisor?
Yes. The quotient comes out as 0 and the remainder equals the dividend itself, such as 7 divided by 23 giving a quotient of 0 with a remainder of 7.
How do I check a long division answer is correct?
Multiply the quotient by the divisor and add the remainder; the result should equal the original dividend. This calculator shows that check alongside the answer.
For dividing where the result is expressed as a fraction rather than a quotient and remainder, see the fraction calculator. To round a decimal division result to a set number of places, see the rounding calculator.