Long Division Calculator

Perform long division with step-by-step work shown. Displays quotient, remainder, and decimal result.

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Dividend

Divisor

Quotient

Enter dividend and divisor

Remainder

Decimal Result

Verification

Divides Evenly

Step-by-step Long Division

Divide any two whole numbers and see the full long-division work shown digit by digit, alongside the quotient, remainder, and decimal result.

How It Works

How Long Division Calculator Works

The quotient is the whole-number result of dividend ÷ divisor (rounded down), and the remainder is whatever is left over after that division — the calculator computes both directly, then also gives the exact decimal result carried out to eight places.

The step-by-step panel reconstructs the same process you'd use by hand: it brings down one digit of the dividend at a time, divides the running total by the divisor at each stage to get the next quotient digit, subtracts, and carries the remainder forward to combine with the next digit.

A verification line confirms the result using divisor × quotient + remainder = dividend, and a badge flags whether the division comes out even (remainder of zero) or leaves a remainder.

Worked Example

See It In Action

Dividing 137 ÷ 5: 5 goes into 13 two times with 3 left over; bringing down the 7 makes 37, and 5 goes into 37 seven times with 2 left over. So the quotient is 27 with a remainder of 2 — verified by 5 × 27 + 2 = 137. As a decimal, 137 ÷ 5 = 27.4 exactly.

Real-World Use Cases

Who Uses Long Division Calculator and Why

Checking a student's hand-worked long division step by step, digit by digit, against the calculator's version.
Splitting a total quantity into equal whole groups while also seeing exactly how many items are left over.
Converting a fraction into its exact decimal form carried out to eight places.
Verifying a division result using the divisor × quotient + remainder = dividend check shown alongside the answer.

Common Mistakes

Mistakes to Avoid

Reading the remainder as if it were the decimal portion of the answer — 137 ÷ 5 has a remainder of 2, but a decimal result of 27.4; the two numbers answer different questions.
Assuming a non-zero remainder means the division "failed" — it just means the divisor doesn't fit evenly, which the calculator flags clearly rather than treating as an error.
Overlooking the verification line (divisor × quotient + remainder = dividend) as a quick way to confirm the result rather than re-deriving it by hand.

Pro Tips

Tips for Best Results

Use the remainder when you need a "how many full groups and how many left over" answer, and the decimal result when you need the precise fractional value.
Check the "Divides Evenly" badge first for a quick yes/no on whether the divisor fits the dividend with nothing left over.

Troubleshooting

Fixing Common Problems

The divisor is larger than the dividend. — That's a valid input — the quotient will simply be 0 and the remainder will equal the original dividend, since the divisor doesn't fit even once.

My hand-worked remainder doesn't match the calculator's. — Re-check each step where you bring down the next digit and subtract — a single missed carry-down early in long division throws off every later digit.

Glossary

Terms Explained

Quotient: The whole-number result of dividend ÷ divisor, rounded down.

Remainder: What's left over after dividing out the largest possible whole number of times.

FAQ

Frequently Asked Questions

What's the difference between the remainder and the decimal result?

The remainder is the whole number left over after integer division (useful for things like "how many full boxes and how many left over"), while the decimal result continues the division into fractional parts — 137 ÷ 5 has remainder 2, but decimal 27.4.

How do I know if a division comes out evenly?

If the remainder is 0, the divisor divides the dividend exactly with nothing left over; the calculator flags this directly with a "Divides Evenly" badge.

Can the divisor be larger than the dividend?

Yes — the quotient will simply be 0 and the remainder will equal the original dividend, since the divisor doesn't fit into it even once.

How is the digit-by-digit process shown?

The calculator brings down each digit of the dividend in turn, just as in a hand-worked long division problem, showing the subtraction and remainder at every step until all digits have been used.