About this Long Division
Long division is a standard arithmetic procedure for dividing simple or complex multidigit numbers. Unlike standard calculators that give you a decimal result, this tool provides the 'Remainder', which is essential for modular arithmetic and breaking down quantities into whole units.
Who this calculator is for
- Students practicing quotient-and-remainder problems.
- Parents and teachers checking long-division homework.
- Programmers who need to verify integer division and modulo results.
When to use it
- Use it when you need a whole-number quotient plus a remainder instead of a decimal answer.
- Use it to check whether one number divides evenly into another.
- Use it before converting a remainder into a fraction, decimal, or modulo expression.
How to use this calculator
- Enter the Dividend (the number being divided).
- Enter the Divisor (the number you are dividing by).
- The result shows the Quotient (whole number result) and the Remainder.
Key assumptions
- This calculator is for integer division, so both inputs must be whole numbers.
- Division by zero is undefined and returns an invalid state.
- For supported inputs, the result always satisfies Dividend = (Quotient × Divisor) + Remainder.
- When negative numbers are used, the quotient is truncated toward zero and the remainder is computed from that identity.
Accuracy and testing
Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.
How this calculator works
The formula is: Dividend = (Quotient × Divisor) + Remainder.
For example, 10 ÷ 3:
* 3 goes into 10 three times (Quotient = 3).
* 3 × 3 = 9.
* 10 - 9 = 1 (Remainder = 1).
Inputs explained
Dividend
The amount that you want to divide up.
Divisor
The number you are dividing by.
Understanding your results
The result is displayed as Quotient R Remainder (e.g., 3 R 1). For positive inputs, this is equivalent to writing the answer as a mixed fraction: $3 \frac{1}{3}$.
Example scenarios
Simple Division
22 ÷ 5. Quotient: 4. Remainder: 2. (Result: 4 R 2)
Perfect Division
20 ÷ 5. Quotient: 4. Remainder: 0. (Result: 4 R 0)
Key Features
- Remainder Calculation
- Integer Math
- Modulo Helper
Tips & Best Practices
- In computer programming, the remainder operation is called **Modulo** (%).
- If the remainder is 0, the dividend is perfectly divisible by the divisor.
Glossary of Terms
- Quotient
- The result of division.
- Remainder
- The amount left over after division.
- Modulo
- A mathematical operation that returns the remainder of a division.