Long Division Calculator

What Is Long Division?

Long division is a step-by-step method for dividing one number by another. It breaks a large division problem into a sequence of smaller, manageable steps: divide, multiply, subtract, and bring down. The method works for any pair of integers and produces a quotient along with a remainder if the division is not exact.

The algorithm dates back centuries and is still taught because it reveals the structure of division in a way that a calculator answer alone cannot. When you type 847 divided by 23 into a phone and get 36.7826..., you learn nothing about why that answer is correct. Working through the long division steps shows exactly where each digit of the quotient comes from and why the remainder is what it is.

For problems involving fractions rather than whole-number division, use our Fraction Calculator. For the remainder operation specifically, try the Modulo Calculator.

What This Calculator Does

Enter a dividend and a divisor, and this tool performs the full long division while showing every step. Each step displays the digit brought down, the division, the multiplication, and the subtraction that produces the running remainder. If the division does not terminate, the calculator continues into decimal places up to the limit you specify, and it detects repeating decimals.

• Inputs: A dividend (0 or greater) and a divisor (1 or greater), each up to one billion, plus a maximum number of decimal places
• Outputs: The quotient, any remainder, step-by-step worked solution, and repeating decimal detection

How the Calculation Works

Long division processes the dividend one digit at a time from left to right. At each stage, the algorithm performs four operations:

1. Bring down: Append the next digit of the dividend to the current working remainder. If no digits remain and the remainder is not zero, bring down a 0 and begin the decimal portion of the quotient.
2. Divide: Determine how many times the divisor fits into the current working number. This is the next digit of the quotient.
3. Multiply: Multiply the quotient digit by the divisor.
4. Subtract: Subtract that product from the working number to get the new remainder.

The process repeats until all dividend digits are consumed and the remainder is zero, or until the decimal place limit is reached. A repeating decimal is detected when a remainder recurs, because the same sequence of steps will produce the same quotient digits forever.

Worked Example: 847 / 23

How to Use the Calculator

1. Enter the dividend (the number being divided) in the first field
2. Enter the divisor (the number you are dividing by) in the second field
3. Set the maximum decimal places for non-terminating results (default 10)
4. The quotient, remainder, and full step-by-step solution appear instantly
5. Use the copy button to copy the quotient

Example Calculations

Example 1: 847 / 23

A fifth-grade teacher in Atlanta, Mrs. Chen, uses this calculator on a projector to walk her class through 847 divided by 23. The first digit, 8, is too small for 23, so the quotient starts with 0 and she brings down the 4 to make 84. Then 84 divided by 23 is 3 (since 3 x 23 = 69), leaving a remainder of 15. Bringing down the 7 gives 157, and 157 divided by 23 is 6 (since 6 x 23 = 138), leaving a remainder of 19. The quotient is 36 with a remainder of 19. Her students follow each step on the screen.

Example 2: 1 / 3 (Repeating Decimal)

A college student in Boston studying number theory enters 1 divided by 3 to observe the repeating pattern. The calculator shows: bring down 1, 1 / 3 = 0, decimal point begins, bring down 0, 10 / 3 = 3, 3 x 3 = 9, 10 - 9 = 1. The remainder 1 recurs, so the calculator flags it as a repeating decimal. The quotient is 0.333... with the digit 3 repeating forever. This demonstrates that 1/3 cannot be expressed exactly as a finite decimal.

Example 3: 10000 / 7

An accountant in Chicago needs to split a $10,000 invoice total across 7 projects evenly. She enters 10000 divided by 7. The calculator produces 1428.571428... and detects the repeating block 571428. Each project gets $1,428.57, and she notes the remainder to handle the rounding difference in her ledger. The repeating block of 6 digits is a property of dividing by 7 that appears in many practical contexts.

Real-World Scenarios

Splitting Costs Evenly

A group of 13 friends in Seattle rents a vacation house for $4,875 for the week. To split the cost evenly, one of them uses this calculator to divide 4875 by 13. The steps show: 48 / 13 = 3 (remainder 9), bring down 7 to make 97, 97 / 13 = 7 (remainder 6), bring down 5 to make 65, 65 / 13 = 5 (remainder 0). Each person owes $375 exactly. The step-by-step output lets her verify the math before sending payment requests.

Unit Conversion in Construction

A contractor in Denver needs to cut a 144-inch board into 11 equal shelves. He divides 144 by 11 using this calculator. The result is 13.0909... inches per shelf, with the decimal 09 repeating. Since he cannot cut to a repeating decimal, he rounds to 13.09 inches and notes that the last shelf will be slightly longer. The worked steps help him explain the measurement to his apprentice.

Understanding Repeating Decimals

A math tutor in Austin uses this calculator to show students why some fractions terminate and others repeat. Dividing 1 by 4 gives 0.25 exactly, because 4 divides evenly into powers of 10. Dividing 1 by 6 gives 0.1666..., because 6 has a factor of 3 that does not divide 10. The calculator detects the repeating remainder and marks the result, making the pattern visible rather than hiding it behind a rounded display.

Common Mistakes to Avoid

• Bringing down digits out of order: Always process the dividend from left to right, one digit at a time. Skipping or reordering digits produces a wrong quotient.
• Forgetting to place the decimal point: When the dividend runs out but a remainder remains, you must add a decimal point to the quotient and a zero to the working remainder. Forgetting this step is a common source of errors in manual long division.
• Misplacing the quotient digits: Each quotient digit must align with the last digit brought down. If you bring down two digits at once (because the first was too small), the quotient digit still corresponds to the position of the last digit brought down.
• Stopping too early: A remainder of zero means the division is exact and you can stop. A non-zero remainder with no more digits to bring down means you either report the remainder or continue into decimal places. Stopping at a non-zero remainder without reporting it loses information.

Limitations of This Calculator

This calculator handles positive integers up to one billion for both dividend and divisor. It does not accept negative numbers or decimals as inputs, though it produces decimal outputs when the division does not terminate. The decimal place limit prevents infinite loops on repeating decimals, and the repeating detection identifies when a quotient has a recurring pattern. For division involving fractions, mixed numbers, or negative values, use the Fraction Calculator or Scientific Calculator.

Authoritative Research & Resources

• LibreTexts Mathematics - Arithmetic - A peer-reviewed open-access resource covering the long division algorithm, its mathematical foundations, and worked examples. Suitable for both students learning the method and teachers preparing lessons.
• Khan Academy - Arithmetic - Free video lessons and practice exercises on long division, including multi-digit divisors, decimal quotients, and repeating decimals. The exercises progress from basic to advanced problems.
• National Council of Teachers of Mathematics (NCTM) - The professional organization for math educators, with standards and research on how students learn division concepts. NCTM's Principles and Standards guide how long division is taught in U.S. schools.
• Maths Is Fun - Long Division - A clear reference with animated examples of the long division process, covering remainders, decimal results, and the relationship between division and multiplication.