Long Division Calculator

Perform long division with a detailed step-by-step breakdown.

Enter the dividend and divisor to see the complete solution, including the quotient and remainder.

Examples

Try these examples to see how the calculator works.

Basic Division

example

A simple division problem with whole numbers.

Dividend: 100

Divisor: 10

Precision: 0

Division with Remainder

example

An example where the division results in a remainder.

Dividend: 101

Divisor: 10

Precision: 2

Large Numbers

example

Dividing larger numbers to see the full process.

Dividend: 12345

Divisor: 67

Precision: 4

Dividend Smaller Than Divisor

example

An example where the dividend is smaller than the divisor.

Dividend: 5

Divisor: 10

Precision: 1

Other Titles
Understanding Long Division: A Comprehensive Guide
A complete overview of the long division process, its applications, and mathematical principles.

What is Long Division?

  • The Core Concept
  • Key Terminology
  • Why It's Important
Long division is a standard algorithm used for dividing multi-digit numbers. It breaks down a complex division problem into a series of smaller, more manageable steps. This method is fundamental in arithmetic and is essential for solving division problems that aren't easily done mentally.
Key Terminology
To understand long division, you need to know its parts: the dividend (the number being divided), the divisor (the number you are dividing by), the quotient (the result), and the remainder (what's left over).
Why It's Important
Long division is a foundational skill that helps in understanding fractions, decimals, and more complex algebraic concepts. It builds number sense and problem-solving skills.

Basic Examples

  • 144 ÷ 12 = 12
  • 256 ÷ 16 = 16

Step-by-Step Guide to Using the Long Division Calculator

  • Inputting Your Numbers
  • Interpreting the Results
  • Following the Steps
Our calculator simplifies the long division process. Here's how to use it effectively:
Inputting Your Numbers
Enter the dividend and the divisor into their respective fields. The dividend is the number you want to divide, and the divisor is the number you are dividing by. Select the desired decimal precision for the quotient.
Interpreting the Results
After clicking 'Calculate', the tool will display the quotient and the remainder. The quotient is the main result of the division, while the remainder is the value left over when the division is not exact.
Following the Steps
The calculator provides a detailed, step-by-step breakdown of the division process. This allows you to follow the logic from the initial division to the final remainder, making it a great learning tool.

Calculation Example

  • Dividend: 500, Divisor: 15 -> Quotient: 33, Remainder: 5

Real-World Applications of Long Division

  • Resource Allocation
  • Financial Planning
  • Event Planning
Long division isn't just a classroom exercise; it has many practical uses.
Resource Allocation
Imagine you have 200 apples to distribute among 15 families. Long division helps you determine that each family gets 13 apples, with 5 apples remaining.
Financial Planning
If you want to save $5,000 for a trip over 12 months, long division can calculate that you need to save approximately $416.67 per month.
Event Planning
Planning a banquet for 150 guests with tables that seat 8 people each requires division to figure out you need 19 tables (18 full and one with 6 guests).

Practical Scenario

  • Splitting a bill of $128 among 4 friends: $128 ÷ 4 = $32 each.

Common Misconceptions and Correct Methods

  • Handling Remainders
  • Decimal Placement
  • Forgetting to Bring Down
Several common mistakes can occur when performing long division manually. Understanding them helps improve accuracy.
Handling Remainders
A common mistake is forgetting the remainder or treating it as a decimal incorrectly. The remainder is a whole number that is less than the divisor.
Decimal Placement
When dividing into decimals, placing the decimal point in the quotient correctly is crucial. It should align directly above the decimal point in the dividend.
Forgetting to Bring Down
A key step is bringing down the next digit from the dividend. Forgetting this step will lead to an incorrect result. Our calculator automates this to prevent errors.

Common Error Example

  • Incorrect: 101 ÷ 10 = 10.0. Correct: 101 ÷ 10 = 10 with a remainder of 1.

Mathematical Principles Behind Long Division

  • The Division Algorithm
  • Place Value
  • Iterative Subtraction
Long division is based on the division algorithm, which states that for any integers a (dividend) and b (divisor), there exist unique integers q (quotient) and r (remainder) such that a = bq + r and 0 ≤ r < |b|.
Place Value
The method heavily relies on the principle of place value (ones, tens, hundreds, etc.). Each step of long division deals with a specific place value, moving from left to right.
Iterative Subtraction
At its core, division is a form of repeated subtraction. Long division is an efficient and organized way of performing these subtractions in chunks (by multiplying the divisor by a digit in the quotient).

Algorithm Example

  • For 25 ÷ 7: q=3, r=4. This fits the formula 25 = 7 * 3 + 4.