Division Calculator

Enter a dividend and divisor to get the whole-number quotient, remainder, and full decimal result — worked out the same way as long division on paper.

Quick Facts

Division identity
Dividend = Divisor × Quotient + Remainder
The remainder is always smaller in size than the divisor.
Decimal quotient
Decimal Quotient = Dividend ÷ Divisor
Same as continuing long division past the decimal point.
Divisor rule
Divisor ≠ 0
Division by zero is undefined.

Your Results

Calculated
Quotient (whole number)
-
Times the divisor fits into the dividend
Remainder
-
What's left over after the quotient
Decimal Quotient
-
Dividend ÷ Divisor, in full decimal form
Check
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Divisor × Quotient + Remainder

Ready

Enter a dividend and divisor, then press Calculate.

How Long Division Works

Long division breaks one number (the dividend) into equal groups sized by a second number (the divisor), producing a whole-number quotient and whatever is left over, the remainder. Every division problem obeys the identity Dividend = Divisor × Quotient + Remainder, with the remainder always smaller in size than the divisor. This calculator gives you the whole-number quotient and remainder, plus the full decimal quotient you'd get by continuing the division past the decimal point.

Formula and method

Given a dividend and a non-zero divisor, the calculator first finds the whole-number quotient — how many complete times the divisor fits into the dividend — by truncating dividend ÷ divisor toward zero. It then finds the remainder with Remainder = Dividend − (Divisor × Quotient). This mirrors the manual algorithm: at each step you estimate how many times the divisor fits into the current digits, subtract that multiple, and bring down the next digit until nothing is left to bring down. The decimal quotient is simply Dividend ÷ Divisor computed directly, which is equivalent to continuing that same process with zeros brought down after the decimal point.

Common sources of error

  • Swapping dividend and divisor: 15 ÷ 987 and 987 ÷ 15 give very different answers — the dividend goes on top (or inside the division bracket), the divisor outside.
  • Remainder too large: a correct remainder is always smaller than the divisor; if yours isn't, the quotient's last digit is too small.
  • Losing the decimal point: when converting a remainder to a decimal, keep careful track of place value — a misplaced decimal point changes the answer by a factor of 10.

Checking your result

Multiply the divisor by the quotient and add the remainder — the result should equal the original dividend exactly (Divisor × Quotient + Remainder = Dividend). This calculator shows that check alongside the results so you can confirm it at a glance.

Applications

Long division shows up whenever a total needs to be split into equal whole parts: dividing a bill among diners, converting a fraction to a decimal, figuring out how many full boxes a shipment fills (with leftovers as the remainder), or computing unit rates like miles per gallon. In computer science, the quotient and remainder from integer division are the basis of the modulo operation used in scheduling, hashing, and array indexing.

Frequently Asked Questions

What is the formula for long division?
Dividend = Divisor × Quotient + Remainder, where the remainder is always smaller in size than the divisor. For example, dividing 987 by 15 gives a quotient of 65 and a remainder of 12, since 15 × 65 + 12 = 987.
How do you find the remainder in long division?
First find the whole-number quotient (how many whole times the divisor fits into the dividend), then subtract: remainder = dividend − (divisor × quotient). The remainder must always be smaller in magnitude than the divisor.
How do I turn a long division remainder into a decimal?
Divide the dividend by the divisor directly (dividend ÷ divisor) instead of stopping at the whole-number quotient and remainder. This continues the division past the decimal point, which is the same as bringing down zeros after the remainder in a paper long division problem.
Can you do long division with negative numbers?
Yes. Divide the numbers as if both were positive, then apply the sign rules: the quotient is negative if exactly one of the dividend or divisor is negative. This calculator follows the standard truncated-division convention, where the remainder takes the same sign as the dividend.

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