Remainders answer “how many are left over?” – 17 eggs in boxes of 6 leave 5. They also decide odd and even, days of the week and clock times.
How to use the Remainder Calculator
- Dividend
- Divisor
Results update as you type, and everything is calculated in your browser.
How it works
The quotient is the whole number of times the divisor fits; the remainder is what is left and is always smaller than the divisor.
Tips
- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.
Common mistakes to avoid
- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.
Inputs explained
| Field | What to enter |
|---|---|
| Dividend | A number |
| Divisor | A number |
What each result means
- Remainder = [Dividend] – [Divisor]×floor([Dividend]÷[Divisor])
- Quotient = floor([Dividend]÷[Divisor])
- Check: divisor × quotient + remainder = [Divisor]×floor([Dividend]÷[Divisor]) + ([Dividend] – [Divisor]×floor([Dividend]÷[Divisor]))
Example values
How the main result changes when Dividend changes and everything else stays at the example values above:
| Dividend | Remainder |
|---|---|
| 8.5 | 2.5 |
| 12.75 | 0.75 |
| 17 | 5 |
| 21.25 | 3.25 |
| 25.5 | 1.5 |
| 34 | 4 |
Formula
Remainder = dividend − divisor × ⌊dividend ÷ divisor⌋
Worked example
Inputs — Dividend: 17; Divisor: 6.
Results — Remainder = 5; Quotient = 2; Check: divisor × quotient + remainder = 17.
Key terms
- Remainder
- The amount left after whole-number division.
Frequently asked questions
What is the remainder of 17 ÷ 6?
5.
Can the remainder be larger than the divisor?
No – if it were, the divisor would fit once more.
What does a remainder of 0 mean?
The divisor divides the dividend exactly.
How is the remainder written?
17 ÷ 6 = 2 R 5.
What formula does the Remainder Calculator use?
Remainder = dividend − divisor × ⌊dividend ÷ divisor⌋.