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Long Division Calculator

Divide whole numbers with quotient, remainder, decimal result, and long division steps.

  • long division
  • quotient remainder
  • division steps
  • divide whole numbers
  • remainder calculator

The number being divided.

The number to divide by. It cannot be zero.

How many decimal places to show for the decimal result.

Status: initial

Results

Awaiting calculation

Explore your result

Quotient and remainder

Explore the long division calculator result visually while keeping this page's detailed guidance and examples.

Quotient and remainder
Quotient12
Remainder3
Decimal result12.38

Use this result well

  1. 1Verify the calculator inputs.
  2. 2Compare the key result relationships.
  3. 3Review the page guidance before acting.

Multiply the divisor by the quotient and add the remainder to verify the result.

Calculator guide

Introduction

The Long Division Calculator divides whole numbers and shows the quotient, remainder, decimal result, simplified fraction form, repeating decimal notation, check equation, and school-style long division steps.

What is long division?

Long division is a written method for dividing a dividend by a divisor. It breaks the problem into repeatable divide, multiply, subtract, and bring-down steps so the quotient and remainder can be checked by hand.

Long division method

At each step, bring down the next digit, divide the partial dividend by the divisor, multiply back, subtract, and carry the remainder forward. If there is a remainder, the calculator can continue into decimal places by adding zeros after the decimal point.

Variable explanations

Understand what each input and result means before calculating.

Dividend

The number being divided.

Divisor

The number you divide by. It cannot be zero.

Quotient

The whole-number result of division.

Remainder

The amount left over after whole-number division.

Partial dividend

The current number being divided in a long division step.

Product

The quotient digit multiplied by the divisor.

Decimal digit

The digit found by continuing division after the decimal point.

Check equation

The multiplication statement used to verify the answer.

Reviewed by the Calculator.org.in Editorial Team

Formula behavior, validation cases, explanatory examples, and cited sources are checked before publication. This review supports educational accuracy and is not a substitute for qualified professional advice.

Last reviewed: 2026-08-03

Review process

Formula guide

See the calculation logic, variable definitions, and practical meaning.

Remainder form

Dividend = divisor x quotient + remainder

  • The remainder must be less than the divisor.

Use this to check any quotient and remainder answer.

Decimal form

Decimal result = dividend / divisor

  • Decimal places control displayed precision.

Use this when you need an approximate decimal quotient.

Mixed-number form

Dividend / divisor = quotient + remainder / divisor

  • The fraction part can be simplified by the greatest common divisor.

Use this when a remainder answer should also be shown as a fraction.

Long division cycle

Divide, multiply, subtract, bring down

  • Each digit of the dividend is processed from left to right.

This is the school-style workflow shown in the step table.

Decimal continuation

New partial dividend = remainder x 10

  • A zero is brought down after the decimal point.

Repeat this to generate decimal digits after the whole-number quotient.

Terminating decimal check

A simplified denominator with only factors 2 and 5 terminates

  • The denominator is the divisor after simplifying the remainder fraction.

Other denominators create repeating decimals.

Remainder rule

0 <= remainder < divisor

  • The divisor must be positive.

If the remainder is equal to or greater than the divisor, the quotient is too small.

Worked examples

Follow realistic inputs through the calculation step by step.

1

Worked example

845 divided by 6

  1. 1845 / 6 = 140 R 5.
  2. 2The decimal is 140.8(3), meaning the 3 repeats.
  3. 3Check: 6 x 140 + 5 = 845.
2

Worked example

100 divided by 7

  1. 1100 / 7 = 14 R 2.
  2. 2The decimal repeats as 14.(285714).
  3. 3The remainder fraction is 14 2/7.
3

Worked example

Even division

  1. 1144 / 12 = 12 R 0.
  2. 2The decimal terminates at 12.
  3. 3The simplified fraction result is 12.
4

Worked example

Simplified remainder fraction

  1. 118 / 12 = 1 R 6.
  2. 2The remainder fraction 6/12 simplifies to 1/2.
  3. 3The mixed-number result is 1 1/2.

Common mistakes

Avoid these common input and interpretation errors.

Dividing by zero

A divisor cannot be zero because division by zero is undefined.

Forgetting zero quotient digits

Some steps need a 0 digit in the quotient when the partial dividend is smaller than the divisor.

Confusing dividend and divisor

In dividend / divisor, the dividend is the number being divided and the divisor is the number dividing it.

Leaving a large remainder

The remainder should always be smaller than the divisor.

Stopping before the decimal point

If you need a decimal answer, continue by bringing down zeros after the decimal point.

Treating a repeating decimal as exact

A rounded decimal such as 0.3333 is approximate; 0.(3) or 1/3 is exact.

Skipping the check equation

Always verify with divisor x quotient + remainder = dividend.

Frequently asked questions

Quick answers to the questions users ask most often.

What does this Long Division Calculator do?
It divides whole numbers and shows quotient, remainder, decimal result, simplified fraction result, repeating decimal notation, and step-by-step long division work.
What is the dividend?
The dividend is the number being divided.
What is the divisor?
The divisor is the number you divide by.
What is the quotient?
The quotient is the whole-number result of division.
What is the remainder?
The remainder is the amount left over after whole-number division.
Can the divisor be zero?
No. Division by zero is undefined.
Can I use decimals as inputs?
This calculator is focused on whole-number long division with remainder. It also shows decimal output for the whole-number division problem.
What is the long division cycle?
Divide, multiply, subtract, bring down, and repeat.
How do I check a remainder answer?
Use dividend = divisor x quotient + remainder.
Should the remainder be smaller than the divisor?
Yes. If it is not, the quotient can be increased.
What does 845 divided by 6 equal?
It equals 140 R 5, or approximately 140.8333. The repeating decimal form is 140.8(3).
Can this show decimal places?
Yes. Choose 0 to 8 decimal places for the rounded decimal result.
What does repeating decimal notation mean?
Digits inside parentheses repeat forever. For example, 0.(3) means 0.3333...
Why are some quotient digits zero?
A zero digit appears when a brought-down partial dividend is smaller than the divisor.
What is a partial dividend?
It is the current number formed during long division after bringing down the next digit.
What is decimal continuation?
It continues division after the decimal point by multiplying the remainder by 10 and dividing again.
When does a decimal terminate?
A simplified denominator with only factors of 2 and 5 creates a terminating decimal.
When does a decimal repeat?
A decimal repeats when the division reaches a remainder that has already appeared.
How do I simplify the remainder fraction?
Divide the remainder and divisor by their greatest common divisor.
Is long division still useful?
Yes. It explains how division works and provides a reliable way to check division problems by hand.
Does this handle polynomial long division?
No. This calculator handles whole-number arithmetic long division.

References

Sources used to support the calculator guidance.

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Version history

A transparent record of calculator content updates.

Updated 2026-08-03
  • 1.1.0 · 2026-08-03

    Added simplified fraction result, check equation, repeating decimal notation, decimal continuation steps, place value summary, and expanded long-division guidance.

  • 1.0.0 · 2026-07-06

    Initial long division calculator release.