Enter two integers to find the quotient and the remainder. You will also see the full check using a = b × q + r, so it is easy to understand where the answer comes from.
Remainder Calculator
Dividend and divisor
Use whole numbers only. The divisor cannot be zero.
How to use the calculator
- Type the number to be divided in the Dividend field.
- Type the number you are dividing by in the Divisor field. It must not be zero.
- Select Calculate to see the integer quotient, the remainder and the check.
- Select Clear when you want to start a new calculation.
What quotient and remainder mean
In Euclidean division, an integer a divided by a nonzero integer b can always be written as a = b × q + r, with 0 ≤ r < |b|.
a = b × q + r, 0 ≤ r < |b|
- a is the dividend — the number being divided.
- b is the divisor — the number you divide by.
- q is the quotient — the whole-number result.
- r is the remainder — the amount left over; it is never negative and is smaller than |b|.
If r = 0, the division is exact. In that case, b divides a evenly and a is a multiple of b.
Worked examples
| Dividend (a) | Divisor (b) | Quotient (q) | Remainder (r) | Check |
|---|---|---|---|---|
| 17 | 5 | 3 | 2 | 3 × 5 + 2 = 17 ✓ |
| 30 | 7 | 4 | 2 | 4 × 7 + 2 = 30 ✓ |
| 48 | 6 | 8 | 0 | 8 × 6 + 0 = 48 ✓ |
| 100 | 9 | 11 | 1 | 11 × 9 + 1 = 100 ✓ |
Frequently asked questions about remainders
What are the quotient and remainder?
The quotient is the whole-number result of the division. The remainder is what is left after forming all possible complete groups. Together they satisfy a = b × q + r.
How do I check an integer division?
Multiply the quotient by the divisor and add the remainder. If the result equals the dividend, the division is correct.
Can the remainder be zero?
Yes. A zero remainder means the division is exact. For example, 12 ÷ 4 has quotient 3 and remainder 0.
Can the quotient be negative?
Yes. The quotient is negative when the dividend and divisor have opposite signs. In Euclidean division, the remainder itself stays nonnegative.
How is Euclidean division different from decimal division?
Euclidean division gives an integer quotient plus a remainder. Decimal division expresses the same operation as a fraction or decimal, such as 7 ÷ 2 = 3.5.
See also…
