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Long Division Calculator: Steps, Remainder, Decimal

Aniruddh

September 9, 2025

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Long Division Calculator

Type two numbers and get the quotient, a non-negative remainder, a clean step-by-step grid, and a rounded decimal. The tool also handles negative numbers and decimals.

Quick answer box

• Input: Dividend ÷ Divisor.
• Output: Integer quotient q, non-negative remainder r with 0 ≤ r < |divisor|, and a decimal expansion.
• Identity: dividend = divisor × q + r (Euclidean division).
• Decimals: The calculator normalizes inputs so the long-division grid stays clear even when either entry has decimal places.

How to use the Long Division calculator

1. Enter the dividend. This is the number you want to divide.
2. Enter the divisor. This is the number you are dividing by. Do not use zero.
3. Set decimal places. Choose how many digits you want in the rounded decimal.
4. Read the results. You will see the integer quotient, the remainder, a neat long-division grid, and a decimal result.
5. Copy or share. Use the buttons to copy the identity or share a link with the filled values.

Tip: The grid shows the classic “bring down” format. You can compare it with any school textbook and the structure will feel familiar.

What is long division? (with formula)

Long division is a reliable pencil-and-paper method to divide one number by another. The procedure breaks a large problem into smaller steps and records each subtraction and bring-down along the way.

The underlying rule is the division algorithm or Euclidean division:

a = b × q + r with 0 ≤ r < |b|

Here a is the dividend, b is the divisor, q is the integer quotient, and r is the remainder. This property is standard in number theory and elementary arithmetic. See accessible explanations from Khan Academy and a formal statement in Euclidean division. Britannica also covers division basics in plain language here.

Worked examples you can follow

Example 1: 55 ÷ 3

You know the answer lands between 18 and 19. The grid shows each subtraction cleanly.

 18 —— 3|55 -3 — 25 -24 — 1

• Quotient: 18
• Remainder: 1
• Identity: 55 = 3 × 18 + 1
• Decimal: 18.(3)

Example 2: 532 ÷ 14

 38 ——— 14|532 -28 — 252 -252 — 0

• Quotient: 38
• Remainder: 0
• Decimal: 38

Example 3: 5.5 ÷ 0.3

Both numbers have decimals. The calculator normalizes them first so the grid stays readable. It multiplies each by 10 and uses 55 ÷ 3 for the visual steps. The final numeric result stays the same.

• Quotient: 18
• Remainder: 1 (on the normalized grid)
• Decimal: 18.(3)

Example 4: −10 ÷ 3

You still get a non-negative remainder. The quotient carries the sign.

• Quotient: −4
• Remainder: 2
• Check: −10 = 3 × (−4) + 2

Decimals and repeating decimals

Every rational number has a decimal expansion that either terminates or repeats. When the denominator in simplest form has only 2s and 5s in its prime factorization, the decimal terminates. Otherwise a repeating block appears. This is a standard result in elementary number theory.

The calculator flags a repeating pattern in the “Decimal expansion” note. You still pick how many digits to round to in the main decimal field.

Handling negative numbers and the remainder

Long division does not break when signs change. The quotient takes the combined sign. The remainder stays between 0 and |divisor|−1. This choice is the Euclidean remainder. It gives clean algebra and consistent identities across cases.

Here are quick checks:

• 7 ÷ −3 → quotient −3, remainder 1.
• −7 ÷ 3 → quotient −3, remainder 2.
• −7 ÷ −3 → quotient 3, remainder 2.

The identity a = b × q + r holds in each case. The remainder stays non-negative.

Manual long-division method (step-by-step)

You can still work problems by hand. The method follows a predictable rhythm. Try it with an example. The calculator mirrors these moves line by line.

1. Divide. Look at the smallest left chunk of the dividend that the divisor fits into at least once. Write the first digit of the quotient above the bar.
2. Multiply. Multiply the divisor by that quotient digit.
3. Subtract. Subtract the product from the current chunk. The result becomes the remainder for this cycle.
4. Bring down. Pull down the next digit of the dividend next to the remainder. Repeat the cycle until you run out of digits.
5. Stop or continue. If the remainder is zero then you are done. If not then you have the integer quotient and remainder. You can continue into decimal places by adding zeros after a decimal point.

That rhythm never changes. It works on three-digit examples and on nine-digit ones. It even works when you continue after the decimal point.

Common mistakes and quick tips

• Dividing by zero. Division by zero is undefined. Use any other divisor.
• Forgetting the sign. Apply the sign to the quotient not to the remainder.
• Misplacing the first quotient digit. Start above the first chunk large enough for the divisor to fit. That first placement controls alignment for the rest.
• Skipping normalization for decimals. If the inputs have decimals then multiply both by the same power of ten before drawing the grid. The calculator does this automatically.
• Rounding too early. Do the whole long-division grid with integers. Round once when you present the decimal result.

Frequently asked questions

Can I divide numbers with decimals?

Yes. Multiply both numbers by the same power of ten to remove decimal points then perform the integer long division. The calculator performs this normalization for the grid then reports the decimal result at the precision you choose.

What happens when the decimal repeats?

The decimal expansion of a rational number either terminates or repeats. When it repeats you can write a repeating block in parentheses like 0.(3). You can still round to any number of places for a quick answer.

How do negative inputs affect the remainder?

The calculator uses the Euclidean remainder which is always non-negative. It keeps 0 ≤ r < |b|. This convention makes identities simple and avoids confusion across sign cases. The approach matches the common number theory definition of division with remainder.

Why does the grid sometimes show integer versions of my decimals?

That is normalization. A pair like 5.5 ÷ 0.3 becomes 55 ÷ 3 for the purpose of the handwritten grid. The decimal answer stays the same. The steps are easier to read without decimal points scattered through the layout.

Is there a difference between long division and short division?

Short division skips the write-down of some steps. Long division records each subtract-and-bring-down. For learning and for audit-friendly results long division is preferable.

Troubleshooting and page-speed tips

• Rounding looks off. Increase the decimal place selector for more precision.
• Old results persist. Clear your cache then reload the page. If you use a performance plugin then exclude dynamic modules from minify groups.

Feature highlights at a glance

• Integer quotient and non-negative remainder for every valid input.
• Classic “bring down” long-division grid that mirrors classroom work.
• Rounded decimal with optional repeat-pattern note.
• Support for negatives and for decimal inputs via normalization.
• Copy-ready identity and shareable links.

You can trust long division for any pair of real-world integers. The method writes down each move and reveals the quotient and the remainder in a way that anyone can audit. The calculator on this page speeds up the work and keeps the layout faithful to the classroom grid. Type your numbers and see the result plus the steps.