Long Division Calculator
Divide integers or decimals with exact arithmetic. See the rounded quotient, reduced fraction, remainder for integer inputs, and each long-division step.
Long division formula
For integer division, dividend = divisor × quotient + remainder. With nonnegative integers, the remainder satisfies 0 ≤ remainder < divisor. Decimal inputs are first multiplied by a common power of ten, which preserves their ratio and permits the same integer long-division process.
Checked examples
| Division | Result | Exact information |
|---|---|---|
| 78,945 ÷ 37 | 2,133.64864865 | Integer quotient 2,133; remainder 24 |
| 1 ÷ 8 | 0.125 | Terminating; exact fraction 1/8 |
| 1 ÷ 3 | 0.33333333 | Repeating; exact fraction 1/3 |
| 12.5 ÷ 0.5 | 25 | Decimals normalize to 125 ÷ 5 |
| 5.75 ÷ 2.5 | 2.3 | Terminating; exact fraction 23/10 |
| −17 ÷ 5 | −3.4 | Truncated integer quotient −3; signed remainder −2 |
How to do long division
- Divide the first usable part of the dividend by the divisor.
- Write that quotient digit above the dividend.
- Multiply the divisor by the quotient digit and subtract.
- Bring down the next digit and repeat.
- After the decimal point, append zeros and continue until the remainder is zero or the desired precision is reached.
Rounding, remainders and repeating decimals
- The displayed decimal uses round-half-up at the selected number of places.
- The integer quotient is truncated toward zero. Its signed remainder preserves the identity
a = bq + r. - A reduced fraction terminates only when its denominator contains no prime factors other than 2 and 5.
- Repeating decimals are identified mathematically even when only a limited number of digits are displayed.
Limits
Enter ordinary decimal notation with no commas, spaces, currency symbols, percentages, or scientific notation. Each operand may contain up to 100 digits, excluding the sign and decimal point. The divisor cannot be zero. Up to 30 decimal places and 80 displayed steps are supported.
Frequently asked questions
What is the difference between dividend and divisor?
The dividend is the value being divided. The divisor is the value it is divided by. In 20 ÷ 4 = 5, 20 is the dividend and 4 is the divisor.
Why can the rounded decimal differ from the exact fraction?
A repeating decimal has infinitely many digits. The fraction remains exact, while the decimal display must stop and round at the selected precision.
Can the calculator divide decimals?
Yes. It shifts both decimal points by the same number of places to create an equivalent integer division before generating the quotient digits.
Why is division by zero invalid?
No number multiplied by zero can recover a nonzero dividend, so division by zero is undefined.
Related calculators
Use the Fraction Calculator for fraction operations, the Scientific Notation Calculator for very large or small values, the GCF and LCM Calculator for factors, or the Percentage Calculator for ratios expressed as percentages. Use the Polynomial Calculator for coefficient operations and synthetic division.