# Long Division Calculator

> Divide whole numbers by long division, step by step, and get the quotient, remainder, mixed number and exact repeating decimal.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/long-division-calculator

Long division works through the dividend one digit at a time: bring down a digit, see how many times the divisor fits, subtract, and carry the remainder.

Also called: Division with remainder calculator.

## Inputs
- Dividend (number being divided) (default 1000)
- Divisor (default 7)

## Results
- Answer
- Quotient
- Remainder
- As a mixed number
- Exact decimal (repeating block in brackets)

## Formula

```
Dividend = Divisor × Quotient + Remainder, with 0 ≤ Remainder < Divisor
```

Where:
- Dividend: the number being divided
- Divisor: the number you divide by

## Worked example
1. 10 ÷ 7 = 1, remainder 3; bring down 0 to make 30.
2. 30 ÷ 7 = 4, remainder 2; bring down 0 to make 20.
3. 20 ÷ 7 = 2, remainder 6. Quotient 142, remainder 6; check: 7 × 142 + 6 = 1000.

**Result:** 1000 ÷ 7 = 142 remainder 6, which is 142 6/7 or 142.857142857… with 857142 repeating.

## What the result means

The remainder is what is left over after sharing out equally. Every fraction gives a decimal that either ends or repeats; the repeating block, shown in brackets, is written with a bar over it in many textbooks.

## Assumptions and limits
- Whole-number dividend from 0 to 10¹⁵ and divisor from 1 to 10⁹.
- Repeating blocks longer than 1,000 digits are cut off and marked.

## Questions

### How do I check a long division?

Multiply the quotient by the divisor and add the remainder. You should get the dividend back.

### Why does 1/7 repeat with six digits?

There are only six possible non-zero remainders when dividing by 7, so the remainders, and therefore the digits, must start repeating within six steps.

## Related calculators
- [Fraction Calculator](https://calculators.geekmidst.com/calculators/fraction-calculator)
- [Rounding Calculator](https://calculators.geekmidst.com/calculators/rounding-calculator)
- [Big Number Calculator](https://calculators.geekmidst.com/calculators/big-number-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/long-division-calculator