Free long division calculator
Calculate the quotient and remainder of any integer division — enter a dividend and divisor to see the step-by-step result, updated live, as you type.
On this page10 sections
Integer quotient with remainder. Decimal = dividend / divisor.
Results are estimates. Consult a professional.
How the long division calculator works
Long division breaks a large division problem into a sequence of smaller steps: estimate how many times the divisor fits into a partial dividend, multiply, subtract, bring down the next digit, and repeat. The process yields an integer quotient and remainder, or can be extended to produce a decimal by appending zeros to the dividend and continuing.
Worked example: 153 ÷ 7
Divide 153 by 7. First find the integer quotient and remainder, then extend to a decimal.
Division facts with quotient and remainder
These examples cover a range of dividend and divisor sizes. Each shows the full result: quotient, remainder, and the equivalent mixed-number form.
| Dividend ÷ Divisor | Quotient | Remainder | As decimal |
|---|---|---|---|
| 17 ÷ 5 | 3 | 2 | 3.4 |
| 100 ÷ 7 | 14 | 2 | ≈ 14.286 |
| 256 ÷ 8 | 32 | 0 | 32.0 |
| 153 ÷ 7 | 21 | 6 | ≈ 21.857 |
| 1,000 ÷ 3 | 333 | 1 | ≈ 333.333 |
| 500 ÷ 17 | 29 | 7 | ≈ 29.412 |
| 144 ÷ 12 | 12 | 0 | 12.0 |
| 1,234 ÷ 56 | 22 | 2 | ≈ 22.036 |
Remainders verified by: quotient × divisor + remainder = dividend.
Tips for long division
Long division feels mechanical once you internalise the loop: estimate, multiply, subtract, bring down. These tips smooth out the common sticking points.
- Estimate with rounding — When the divisor is large, round it to the nearest easy number to find the trial digit. Adjust up or down if the product overshoots or undershoots.
- Always verify — Multiply quotient × divisor, add the remainder, and check you get the original dividend. This catches arithmetic slips in seconds.
- Bring down one digit at a time — Never skip digits when bringing down. If the current partial dividend is smaller than the divisor, the next quotient digit is 0 and you bring down another digit.
- Extending to decimals — After the integer quotient, place a decimal point in the answer and append a zero to the remainder, then continue dividing. Repeat for as many decimal places as needed.
- Spotting repeating decimals — If the same remainder recurs during the decimal extension, the decimal repeats. For example, 1 ÷ 7 produces remainders 1, 3, 2, 6, 4, 5, 1, … — the 6-digit block 142857 repeats forever.
Accuracy and limitations
Integer quotient and remainder are exact for any whole-number dividend and divisor. Decimal extension is terminated after a fixed number of places, introducing rounding. When the remainder cycle length exceeds the displayed decimal places, the result is truncated rather than shown with an overbar. For exact fractional results, use a fraction calculator that retains the numerator/denominator form.
Key terms
About this calculator
Part of our math calculators suite — explore all calculators.