Enter the dividend and divisor to find the remainder of an integer division straight away. This focused tool is useful when you need the leftover value rather than a decimal answer.
Division Remainder Calculator
Remainder of an integer division
Use whole numbers only. The divisor cannot be zero.
How to use the calculator
- Enter the number to be divided in the Dividend field.
- Enter the number you are dividing by in the Divisor field. It cannot be zero.
- Select Find remainder. The answer appears in the Remainder field.
- Select Clear to start a new calculation.
What is the remainder of a division?
In Euclidean division, an integer a divided by a nonzero integer b can be written as a = b × q + r. Here q is the integer quotient and r is the remainder, with 0 ≤ r < |b|.
a = b × q + r, 0 ≤ r < |b|
A zero remainder means the division is exact. A nonzero remainder means there is an amount left after making all possible complete groups.
How to calculate the remainder by hand
You can find the remainder in three short steps:
- Divide the dividend by the divisor and keep only the integer quotient q.
- Multiply the divisor by that quotient: b × q.
- Subtract the product from the dividend: r = a − b × q.
Example: for 47 ÷ 8, the integer quotient is 5. Since 8 × 5 = 40, the remainder is 47 − 40 = 7.
Examples
| Dividend | Divisor | Quotient | Remainder | Check |
|---|---|---|---|---|
| 17 | 5 | 3 | 2 | 5 × 3 + 2 = 17 |
| 30 | 7 | 4 | 2 | 7 × 4 + 2 = 30 |
| 48 | 6 | 8 | 0 (exact division) | 6 × 8 = 48 |
| 13 | 2 | 6 | 1 (odd number) | 2 × 6 + 1 = 13 |
Frequently asked questions about division remainders
What is a division remainder?
The remainder is the amount left after the divisor fits into the dividend as many whole times as possible. For 17 ÷ 5, the quotient is 3 and the remainder is 2.
Can the remainder be greater than the divisor?
No. In Euclidean division, the remainder is always at least zero and smaller than the absolute value of the divisor. Otherwise one more complete group could still be formed.
What does a remainder of zero mean?
It means the division is exact. The dividend is a multiple of the divisor, as in 18 ÷ 6 = 3 with remainder 0.
How does the remainder show whether a number is even or odd?
Divide the number by 2. Remainder 0 means the number is even; remainder 1 means it is odd.
What is the modulo operator?
Modulo, written mod in mathematics or % in many programming languages, returns the remainder of an integer division. Thus 17 mod 5 = 2.
See also…
