Long Division Calculator
Divide one whole number by another and see the quotient, remainder, and arithmetic check, the way traditional long division works.
How It's Calculated
Formula
\text{dividend} = \text{divisor} \times \text{quotient} + \text{remainder}Long division splits a dividend into equal groups of a divisor's size, reporting how many whole groups fit (the quotient) and what's left over (the remainder). This calculator handles a non-negative whole-number dividend and a positive whole-number divisor — traditional school-style long division, not decimal or fractional division. The core identity that defines the result is dividend = divisor × quotient + remainder, where the remainder is always smaller than the divisor. This calculator never silently switches to decimal division: if you want a decimal answer instead of a quotient-and-remainder pair, use a general division calculator instead.
Worked Examples
Divide 125 by 4
- 125 ÷ 4
- 4 fits into 125 a total of 31 whole times (4 × 31 = 124)
- 125 − 124 = 1 left over
- Quotient: 31, Remainder: 1
- Check: 125 = 4 × 31 + 1
Divide 100 by 10
- 100 ÷ 10
- 10 fits into 100 exactly 10 times (10 × 10 = 100)
- 100 − 100 = 0 left over
- Quotient: 10, Remainder: 0
- Check: 100 = 10 × 10 + 0
Frequently Asked Questions
What's the difference between the quotient and the remainder?
The quotient is how many whole times the divisor fits into the dividend. The remainder is what's left over after removing that many whole groups — it is always smaller than the divisor. Together they satisfy dividend = divisor × quotient + remainder.
Can I divide by a negative number or divide a negative dividend?
Not with this calculator. This tool uses the traditional school-style convention of a non-negative dividend and a positive divisor, which keeps the quotient/remainder result unambiguous. Signed long division is not supported.
Why isn't the answer a decimal?
Long division intentionally reports a whole-number quotient and a remainder rather than converting the remainder into a decimal fraction — that's the traditional long-division result. This calculator does not silently switch to decimal division.
What happens if I divide by zero?
Division by zero is undefined, so a zero (or non-positive) divisor is rejected as an invalid input.