Remainder Calculator
A remainder calculator shows what is left after one whole number is divided by another. Enter a dividend and divisor, and this page returns the quotient, the remainder, and a check equation so you can see the division worked correctly. It is useful for school math, modular arithmetic, grouping items into equal sets, and quick checks when a division problem does not come out even. A remainder matters any time you care about the leftover part after full groups are counted. If 23 cookies are packed into bags of 5, you can make 4 full bags and 3 cookies remain. The same idea appears in classwork, coding, calendars, clocks, and inventory questions where you need both the number of complete groups and the amount still left over.
Quick answer
The dividend is the number you start with, and the divisor is the number of items in each equal group.
Remainder
3
Quotient
4
Check
5 x 4 + 3 = 23
What this tells you
- •The dividend is the number you start with, and the divisor is the number of items in each equal group.
- •The quotient tells you how many complete groups fit before you run out of the dividend.
- •The remainder is the part that stays left over after all possible complete groups are counted.
- •A valid remainder is always smaller than the absolute value of the divisor, so it can never be large enough to form one more full group.
- •Every result on this page follows the check equation dividend = divisor x quotient + remainder.
- •When the remainder is 0, the division is exact and the divisor is a factor of the dividend.
- •For negative inputs, this calculator keeps the remainder non-negative so the answer matches the Euclidean convention used in number theory.
How to Use
- 1Enter the dividend, which is the whole number you want to divide.
- 2Enter the divisor, which is the whole number you are dividing by. The divisor cannot be 0.
- 3Submit the values to see the remainder first, then the whole-number quotient and the check equation.
- 4Use the check line to confirm the answer. Multiply the divisor by the quotient, then add the remainder to get back to the dividend.
- 5If you are solving a word problem, read the quotient as the number of complete groups and the remainder as the amount left over.
- 6Enter whole numbers only. This tool is built for integer division, not decimal division.
How It Works
Formula
dividend = divisor x quotient + remainder, with 0 <= remainder < |divisor|The calculator uses Euclidean division. First it finds a whole-number quotient based on the division result, then it multiplies that quotient by the divisor and subtracts from the dividend to get the remainder. The final answer must satisfy dividend = divisor x quotient + remainder, and the remainder must be at least 0 and smaller than the absolute value of the divisor. For 23 divided by 5, the quotient is 4 because 5 fits into 23 four complete times. Multiplying back gives 5 x 4 = 20, and subtracting gives a remainder of 23 - 20 = 3. For a negative value such as -17 divided by 5, the calculator adjusts the quotient so the remainder stays non-negative. That is why the result is quotient -4 and remainder 3, since 5 x -4 + 3 = -17.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
23 divided by 5
5 fits into 23 four whole times because 5 x 4 = 20. Subtracting 20 from 23 leaves 3, so the answer is quotient 4 with remainder 3.
100 divided by 7
7 x 14 = 98, which is the largest multiple of 7 that stays at or below 100. The leftover amount is 100 - 98 = 2, so the remainder is 2.
-17 divided by 5
The Euclidean convention keeps the remainder non-negative. Since 5 x -4 = -20 and -20 + 3 = -17, the correct pair is quotient -4 and remainder 3.
52 divided by 13
13 divides evenly into 52 because 13 x 4 = 52 exactly. Nothing is left over, so the remainder is 0 and the quotient is 4.
347 divided by 12
12 x 28 = 336, and the next multiple 12 x 29 = 348 would be too large. Subtracting 336 from 347 leaves 11, so the result is quotient 28 with remainder 11.
Remainders When Dividing by 7
These examples show how the quotient increases and the remainder cycles from 0 to 6 as the dividend changes.
| Dividend | Quotient | Remainder |
|---|---|---|
| 12 | 1 | 5 |
| 14 | 2 | 0 |
| 20 | 2 | 6 |
| 21 | 3 | 0 |
| 100 | 14 | 2 |
| 700 | 100 | 0 |
Common mistakes
- Reading the decimal part as the remainder. In 23 / 5 = 4.6, the remainder is 3, not 6. The decimal part 0.6 represents 3/5.
- Using a remainder that is as large as the divisor. If your remainder equals the divisor or goes past it, another full group still fits and the quotient must increase.
- Skipping the check equation. A quick check with divisor x quotient + remainder catches most simple arithmetic mistakes.
- Forgetting that this tool uses whole-number division only. If you enter decimals, you are no longer working with the standard remainder definition used here.
- Assuming every percent or modulo operator matches the math classroom rule for negative numbers. Many programming languages handle negative values differently.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
<script src="https://calctide.com/embed.js" data-tool="remainder-calculator" async></script>Preview the embed at /embed/remainder-calculator/.