Formula and method
For positive divisor b, choose q and r so a = bq + r with 0 ≤ r < b. This is Euclidean integer division.
Worked example
12,345 divided by 67 gives quotient 184 and remainder 17, since 67 × 184 + 17 = 12,345.
Long Division Calculator
Divide large integers exactly and show the quotient, nonnegative remainder and the identity that verifies the answer.
Printed from Calxy · https://www.calxy.net/math/long-division-calculator
Integer quotient184
Integer quotient
184
- Nonnegative remainder17
- Identity check12345 = 67 × (184) + 17
| Digit step | Partial dividend | Quotient digit | Subtract | Remainder |
|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 |
| 2 | 12 | 0 | 0 | 12 |
| 3 | 123 | 1 | 67 | 56 |
| 4 | 564 | 8 | 536 | 28 |
| 5 | 285 | 4 | 268 | 17 |
Euclidean integer division. For a negative dividend this quotient rounds down, which can differ from programming languages that truncate toward zero.
How this was calculated
Divide the integers exactly with arbitrary precision.
Choose quotient and remainder so dividend = divisor × quotient + remainder and 0 ≤ remainder < divisor.
Frequently asked questions
How are negative dividends handled?
The remainder stays nonnegative. For example, −7 divided by 3 gives quotient −3 and remainder 2, unlike truncation toward zero.
Last updated . Results are estimates for informational purposes only.