Long Division Calculator With Steps and Remainder
Divide whole numbers, decimals, fractions or mixed numbers. The calculator gives the quotient and remainder, exact fraction, mixed number, decimal expansion and each divide–multiply–subtract–bring-down step.
Written and checked by TheToolNet Editorial Team · Last reviewed: August 22, 2026 · How we check math tools
For whole-number division, the remainder is non-negative and smaller than the positive divisor.
Calculate Long Division
Accepted formats include 157, 12.6, 3/4 and 2 1/3. Commas in whole numbers are ignored.
How to do long division
Work from the leftmost dividend digit and repeat four actions:
- Divide: decide how many whole times the divisor fits into the current value.
- Multiply: multiply that quotient digit by the divisor.
- Subtract: subtract the product from the current value.
- Bring down: append the next dividend digit and repeat.
If no digits remain, the leftover value is the remainder. Continue with zeros after a decimal point when a decimal expansion is needed.
Worked example: 157 ÷ 12
12 fits into 15 once. Write 1, multiply 1 × 12 = 12, and subtract to get 3. Bring down 7 to make 37. Then 12 fits into 37 three times; 3 × 12 = 36, leaving 1. Therefore 157 ÷ 12 = 13 remainder 1 = 13 1/12.
The exact check is 12 × 13 + 1 = 157.
Long division with decimals
Shift the decimal point in both numbers by the same number of places until the divisor is a whole number. For 12.6 ÷ 0.3, multiply both numbers by 10 to obtain the equivalent division 126 ÷ 3 = 42.
The calculator performs this conversion with exact fractions, avoiding ordinary binary floating-point rounding. Terminating decimals are shown completely; repeating decimals use parentheses, so 1 ÷ 3 is displayed as 0.(3).
Long division calculator with mixed numbers
Convert each mixed number to an improper fraction, divide by multiplying by the reciprocal, and reduce. For example:
2 1/2 ÷ 3/4 = 5/2 × 4/3 = 10/3 = 3 1/3
Enter mixed numbers with a space between the whole and fractional parts. The fractional part must be proper: use 2 1/3 rather than 2 4/3.
Dividend, divisor, quotient and remainder
| Term | Meaning | In 157 ÷ 12 = 13 R1 |
|---|---|---|
| Dividend | The quantity being divided | 157 |
| Divisor | The quantity dividing the dividend | 12 |
| Quotient | The whole-number result | 13 |
| Remainder | The amount left over | 1 |
Scope and limitations
Inputs may be signed whole numbers, decimals with up to 12 decimal places, fractions, or mixed numbers. The divisor cannot be zero. Written steps operate on an equivalent positive whole-number ratio; the final sign and exact rational result are applied afterward. Extremely long inputs may be inconvenient to display even though integer arithmetic is exact.
Frequently asked questions
What are the four long-division steps?
Divide, multiply, subtract and bring down. Repeat until no dividend digits remain.
How do you find the quotient using long division?
At each position, write the greatest digit whose product with the divisor does not exceed the current value.
Can this calculator divide mixed numbers?
Yes. Use a space, such as 2 1/3. The result includes exact fraction, mixed-number and decimal forms.
What does a repeating decimal in parentheses mean?
The digits inside parentheses repeat forever. For example, 0.(3) means 0.3333….
Related division tools and reference
For algebraic expressions, use the polynomial long division calculator. To calculate an HCF with Euclidean division, use the GCD and LCM calculator.
Method reference: Wolfram MathWorld: Long Division.