Enter Division Values
Use whole numbers only. The calculator compares integer division rules and shows the chosen interpretation clearly.
Example Data Table
| Dividend | Divisor | Mode | Quotient | Remainder | Identity |
|---|---|---|---|---|---|
| 27 | 4 | Euclidean | 6 | 3 | 27 = (4 × 6) + 3 |
| -27 | 4 | Floor | -7 | 1 | -27 = (4 × -7) + 1 |
| -27 | 4 | Truncating | -6 | -3 | -27 = (4 × -6) + -3 |
| 48 | 6 | Euclidean | 8 | 0 | 48 = (6 × 8) + 0 |
Formula Used
Integer division is based on the identity a = bq + r, where a is the dividend, b is the divisor, q is the quotient, and r is the remainder.
- Truncating division: q = trunc(a / b), then r = a − bq.
- Floor division: q = floor(a / b), then r = a − bq.
- Euclidean division: choose q so the remainder satisfies 0 ≤ r < |b|.
- Divisibility test: the dividend is divisible by the divisor when r = 0.
These formulas help compare programming language behavior, mathematical conventions, and sign changes when negative numbers appear in the operation.
How to Use This Calculator
- Enter the dividend as a whole number.
- Enter a nonzero divisor as a whole number.
- Select Euclidean, truncating, or floor division mode.
- Choose whether the result should include worked steps.
- Press the calculate button to show results above the form.
- Review the summary, comparison table, and identity check.
- Use the CSV or PDF buttons to export the result.
Frequently Asked Questions
1. What does integer division return?
Integer division returns a whole-number quotient and a remainder. The exact output depends on the selected rule, especially when negative numbers are involved.
2. Why are there several division modes?
Different mathematical texts and programming languages define quotient rounding differently. This calculator lets you compare truncating, floor, and Euclidean conventions in one place.
3. What is the Euclidean remainder rule?
In Euclidean division, the remainder is always nonnegative and smaller than the divisor’s absolute value. Many number theory problems prefer this form.
4. What happens with negative numbers?
Negative dividends or divisors can change the quotient and remainder depending on the mode. The comparison table highlights those differences clearly.
5. How is divisibility checked?
A number is divisible by the divisor when the selected remainder equals zero. The calculator shows that status instantly in the results area.
6. Can I export the result?
Yes. After calculating, use the CSV button for spreadsheet-friendly data or the PDF button for a clean report you can share or save.
7. Does the calculator support decimals?
No. This tool is designed for whole-number division only. Decimal values should be converted or handled with a different calculator first.
8. Is there any size limit for values?
The calculator uses standard whole-number handling available on the server. Extremely large values may exceed integer limits, depending on the hosting environment.