Remainder Calculator
Enter a dividend and a divisor to get the whole-number quotient and the remainder — the classic “6 R 3” answer from long division, with every step shown.
Example: with Dividend (number being divided) 27 · Divisor (number you divide by) 4 → Remainder: 3.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outQuotient and remainder, step by step
Division with remainders splits a division problem into two whole answers: the quotient (how many times the divisor fits) and the remainder (what’s left over). For 27 ÷ 4, the divisor 4 fits 6 whole times (4 × 6 = 24), leaving 27 − 24 = 3, so the answer is 6 R 3. The check is always quotient × divisor + remainder = dividend: 6 × 4 + 3 = 27.
It’s the everyday way to split things that don’t divide evenly: 100 eggs in cartons of 12 fills 8 cartons with 4 eggs left over. With a positive divisor the remainder always lands between 0 and one less than the divisor — if you ever get a remainder as big as the divisor, the quotient can fit one more time.
How it’s calculated
Quotient = floor(dividend ÷ divisor), the largest whole number of times the divisor fits; remainder = dividend − divisor × quotient. This is floor division, so with a positive divisor the remainder is always 0 ≤ r < divisor even for negative dividends: −7 ÷ 3 gives quotient −3 and remainder 2, since 3 × (−3) + 2 = −7. With a negative divisor the remainder takes the divisor’s sign. A divisor of 0 returns no result because division by zero is undefined.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Reporting the decimal part as the remainder — 27 ÷ 4 = 6.75, but the remainder is 3, not 0.75 (multiply the decimal 0.75 by the divisor 4 to recover it).
- Leaving a remainder equal to or bigger than the divisor — 27 ÷ 4 is 6 R 3, never 5 R 7.
- Trusting a programming language’s % operator for negatives: many truncate toward zero, so −7 % 3 returns −1, while floor division (used here) gives remainder 2.
Frequently asked questions
What is the remainder of 100 divided by 7?
100 ÷ 7 = 14 R 2. Seven fits 14 whole times (7 × 14 = 98), leaving 100 − 98 = 2.
How do I find a remainder without a remainder button?
Divide normally, drop the decimals to get the whole quotient, then compute dividend − divisor × quotient. For 53 ÷ 6: 53 ÷ 6 ≈ 8.83, quotient 8, remainder 53 − 48 = 5.
How are negative numbers handled?
This calculator uses floor division, so the remainder keeps the divisor’s sign: −7 ÷ 3 = −3 R 2, because 3 × (−3) + 2 = −7. Calculators that truncate instead would say −2 R −1 — both satisfy the check equation.
Is remainder the same as modulo?
For positive numbers, yes — 27 mod 4 = 3, the same remainder shown here. They can differ on negatives depending on whether the language floors or truncates the quotient.
Can the dividend be smaller than the divisor?
Yes. The divisor fits zero whole times, so the quotient is 0 and the remainder is the dividend itself: 3 ÷ 8 = 0 R 3.