Long Division Calculator — Free Online Division Tool

How to Use the Long Division Calculator

1. Enter the dividend: Type the number being divided into the first input field. This is the larger number that you want to split into equal groups. The calculator accepts positive and negative integers. For example, if you want to divide 1234 by 7, enter 1234 as the dividend.
2. Enter the divisor: Type the number you are dividing by into the second field. This must be a non-zero integer. If you enter zero, the calculator will display an error since division by zero is undefined. The divisor can also be larger than the dividend, in which case the quotient will be 0.
3. Review the step-by-step work: Below the inputs, the calculator shows every step of the long division algorithm. Each step displays the current number being divided, the divisor, the quotient digit for that step, and the remainder. This follows the traditional "divide, multiply, subtract, bring down" process that you learn in school.
4. Read the results: The results panel displays the integer quotient and remainder prominently, the complete division expression, the full decimal result (with repeating portions shown in parentheses if applicable), whether the decimal repeats, and a verification formula to confirm the answer is correct.

The calculator updates instantly as you type. Negative dividends or divisors are handled correctly — the sign of the result follows standard mathematical rules (negative divided by positive is negative, negative divided by negative is positive).

Long Division Formula

Variables Explained

• Dividend: The number being divided. In the expression 156 / 12, the dividend is 156. It represents the total quantity that you want to distribute equally or split into groups.
• Divisor: The number you divide by. In 156 / 12, the divisor is 12. It represents the number of equal groups or the size of each group, depending on the interpretation. It must not be zero.
• Quotient: The integer result of the division — how many times the divisor fits completely into the dividend. In 156 / 12 = 13, the quotient is 13.
• Remainder: The amount left over after the integer division. It satisfies: 0 less than or equal to Remainder less than |Divisor|. In 157 / 12: quotient = 13, remainder = 1 (since 13 x 12 = 156 and 157 - 156 = 1).

Step-by-Step Example

Divide 4567 by 13 using long division:

1. Bring down 4: 4 / 13 = 0 remainder 4
2. Bring down 5: 45 / 13 = 3 remainder 6 (3 x 13 = 39, 45 - 39 = 6)
3. Bring down 6: 66 / 13 = 5 remainder 1 (5 x 13 = 65, 66 - 65 = 1)
4. Bring down 7: 17 / 13 = 1 remainder 4 (1 x 13 = 13, 17 - 13 = 4)
5. Result: Quotient = 351, Remainder = 4
6. Verify: 351 x 13 + 4 = 4,563 + 4 = 4,567

The decimal result is 351.307692... where the digits 307692 repeat. This means 4567/13 = 351.(307692), a repeating decimal with a 6-digit repeating block.

Practical Examples

Example 1: Tyler's Pizza Party

Tyler orders 7 pizzas with 8 slices each (56 slices total) for 9 friends. He uses long division to find out how many slices each person gets and how many are left over:

• 56 / 9: 9 goes into 56 six times (6 x 9 = 54)
• Quotient: 6 slices per person
• Remainder: 56 - 54 = 2 slices left over
• Verification: 6 x 9 + 2 = 54 + 2 = 56

Each person gets 6 slices with 2 left over. Tyler can eat the extras or cut them in half so 4 people can each have a half-slice more. The integer quotient and remainder give him exactly the information he needs for fair distribution.

Example 2: Lisa's Payroll Calculation

Lisa is a freelancer who earned $8,750 over 12 months and needs to know her average monthly income. She divides 8750 by 12:

• 8750 / 12 = 729 remainder 2
• Integer result: $729 per month with $2 remaining
• Decimal result: $729.1666... ($729.17 rounded to cents)
• Verification: 729 x 12 + 2 = 8,748 + 2 = 8,750

Lisa's average monthly income is approximately $729.17. The remainder of $2 means the annual total does not divide evenly into 12 months — she can allocate the extra $2 to any month she chooses. For more detailed income calculations, she might use our income tax calculator.

Example 3: Marcus's Time Conversion

Marcus has a 4,590-second audio recording and wants to express its length in hours, minutes, and seconds. He uses successive long division:

• 4590 / 3600 = 1 remainder 990 (1 hour, 990 seconds remaining)
• 990 / 60 = 16 remainder 30 (16 minutes, 30 seconds remaining)
• Final result: 1 hour, 16 minutes, 30 seconds
• Verification: 1 x 3600 + 16 x 60 + 30 = 3600 + 960 + 30 = 4,590

Marcus's recording is 1 hour, 16 minutes, and 30 seconds long. This chain-division technique works for any unit conversion involving multiple levels (days/hours/minutes/seconds, feet/inches, etc.). Each division extracts one unit level and passes the remainder to the next.

Division Results Reference Table

Tips and Complete Guide

The Long Division Algorithm Step by Step

Long division follows a repeating four-step cycle: Divide, Multiply, Subtract, Bring Down. First, divide: determine how many times the divisor fits into the current working number (starting with the leftmost digits of the dividend). Second, multiply: compute the divisor times the quotient digit you found. Third, subtract: take the product from the working number to get the remainder for this step. Fourth, bring down: append the next digit from the dividend to the right of the remainder to form the new working number. Repeat these four steps until all digits have been processed. The accumulated quotient digits form the answer, and the final step's remainder is the division remainder.

Understanding Repeating Decimals

A fraction a/b produces a repeating decimal when b has prime factors other than 2 and 5. The maximum length of the repeating block is b-1 digits (for example, dividing by 7 produces at most 6 repeating digits). This is because during the decimal expansion, the remainder at each step must be between 0 and b-1. Once a remainder repeats, the entire cycle of digits that followed will repeat forever. Our calculator detects this by tracking remainders and identifies exactly where the repeating block starts and ends.

Division in Programming and Computer Science

Different programming languages handle integer division differently. In Python 3, the // operator performs floor division (toward negative infinity): -7 // 2 = -4. In C, Java, and JavaScript, integer division truncates toward zero: -7 / 2 = -3 (with parseInt or integer types). This difference matters when working with negative numbers. Our calculator follows the truncation-toward-zero convention, matching most programming languages. Understanding these subtleties prevents bugs when implementing division-based algorithms.

Applications of Long Division Beyond Arithmetic

The long division algorithm extends beyond simple number division. Polynomial long division divides one polynomial by another, essential in algebra and calculus. Synthetic division is a shortcut for dividing polynomials by linear factors. The Euclidean algorithm for finding the greatest common divisor uses repeated division with remainders. Even digital circuit design uses division algorithms for binary arithmetic. The fundamental "divide, compute partial result, find remainder, continue" pattern appears throughout mathematics and computer science. For more advanced mathematical operations, try our scientific calculator.

Common Mistakes to Avoid

• Skipping zeros in the quotient: When the divisor does not fit into the current working number, write a 0 in the quotient and bring down the next digit. Forgetting this zero shifts all subsequent digits, producing a completely wrong answer. For example, 1024 / 5: after the first step gives 2, the next step is 0 / 5 = 0 (not skip).
• Subtraction errors: The most common source of mistakes in long division is simple subtraction errors within the intermediate steps. Double-check each subtraction, especially when borrowing is involved. One wrong subtraction cascades into a completely wrong answer.
• Incorrect first estimate: Estimating how many times the divisor fits can be tricky for multi-digit divisors. If your estimate is too high, the product will exceed the working number (impossible). If too low, the remainder will be larger than the divisor (try the next higher quotient digit). Practice improves estimation speed.
• Forgetting the remainder: Always report the remainder. "1234 / 7 = 176" is incomplete — the correct answer is "176 remainder 2" or "176 R2". The remainder is essential for verification and for applications like distributing items fairly.
• Dividing by zero: There is no meaningful result when the divisor is zero. If you get this error, check that you entered the correct divisor. Division by zero is undefined in all of mathematics.

Frequently Asked Questions