Remainder Calculator
23 divided by 5 is 4 with a remainder of 3, because 5 x 4 = 20 and 3 is left over. This remainder calculator gives you the whole-number quotient and the remainder for any division, plus the check equation that proves the answer. It handles negative numbers using the convention where the remainder is never negative.
Quick answer
The quotient is how many whole times the divisor fits into the dividend.
Remainder
3
Quotient
4
Check
5 x 4 + 3 = 23
What this tells you
- •The quotient is how many whole times the divisor fits into the dividend.
- •The remainder is what is left after those whole fits, always smaller than the divisor.
- •Every answer satisfies dividend = divisor x quotient + remainder.
- •A remainder of 0 means the division is exact and the divisor is a factor.
How to Use
- 1Enter the dividend, the number being divided.
- 2Enter the divisor, the number you are dividing by.
- 3Read the remainder as the main result, with the quotient and check equation below.
- 4Both inputs must be whole numbers, and the divisor cannot be zero.
How It Works
Formula
dividend = divisor x quotient + remainder, with 0 <= remainder < |divisor|Divide and drop everything after the decimal point to get the whole quotient, then multiply back and subtract to find the remainder. For 23 / 5, the quotient is 4 (since 5 goes in 4 whole times) and the remainder is 23 - 20 = 3. For negative dividends the quotient shifts down one so the remainder stays non-negative, which is the convention number theory and clock arithmetic use.
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 (20), leaving 3.
100 divided by 7
7 x 14 = 98, so 2 is left over.
-17 divided by 5
5 x -4 = -20, and -17 minus -20 leaves +3. The remainder stays non-negative.
Remainders When Dividing by 7
How remainders cycle as the dividend grows.
| 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. 23 / 5 = 4.6, but the remainder is 3, not 6. The decimal .6 is 3/5.
- Letting the remainder reach the divisor. If your remainder equals or exceeds the divisor, the quotient needs one more step.
- Trusting a programming language's % operator for negative numbers. Many return -2 for -17 % 5, while the math convention says 3.