Long Division Calculator
Free online calculator with step-by-step solutions for all your division problems
Calculate Long Division
Quick Calculations
Calculation History
Why Use Our Long Division Calculator?
Step-by-Step Solutions
See every step of the long division process with detailed explanations to help you learn.
100% Accurate
Get precise calculations every time with our advanced algorithm that handles any division problem.
Instant Results
Calculate division problems in milliseconds and see results immediately on your screen.
Mobile Friendly
Works perfectly on all devices - smartphones, tablets, and desktop computers.
Remainder Support
Displays both quotient and remainder, with options for decimal conversion.
Calculation History
Keep track of all your calculations with automatic history saving.
What is Long Division?
Long division is a mathematical method for dividing large numbers that breaks down the division process into a series of easier steps. It's one of the most important arithmetic operations taught in elementary and middle school mathematics.
The long division method allows you to divide numbers that would be difficult to divide mentally, and it shows you the complete working process, making it an excellent learning tool for students and anyone who wants to understand division better.
Components of Long Division
- Dividend: The number being divided (inside the division bracket)
- Divisor: The number you're dividing by (outside the division bracket)
- Quotient: The result of the division (above the bracket)
- Remainder: What's left over after division (if the numbers don't divide evenly)
When to Use Long Division
Long division is particularly useful when:
- Dividing large numbers that can't be easily calculated mentally
- You need to show your work step-by-step for homework or exams
- Learning and understanding the division process
- Checking calculator results by hand
- Solving word problems that require division
How to Use the Long Division Calculator
Enter the Dividend
Type the number you want to divide (the dividend) in the first input field. This can be any positive integer or decimal number.
Enter the Divisor
Type the number you want to divide by (the divisor) in the second input field. Make sure this is not zero!
Choose Options
Select whether you want to see detailed steps, decimal results, or animated visualization of the calculation process.
Calculate
Click the "Calculate Division" button to see your results instantly with step-by-step solutions.
Tips for Best Results
- Enter whole numbers for traditional long division problems
- Enable "Show detailed steps" to learn the process
- Use "Show decimal result" for precise decimal answers
- Try the quick calculation buttons for common division problems
- Check your calculation history to review previous problems
Long Division Examples
Example 1: Simple Division
Problem: 156 ÷ 12
Solution:
- 12 goes into 15 once (1 × 12 = 12), write 1 above
- Subtract: 15 - 12 = 3, bring down 6 to make 36
- 12 goes into 36 three times (3 × 12 = 36), write 3 above
- Subtract: 36 - 36 = 0
Answer: 156 ÷ 12 = 13 with remainder 0
Example 2: Division with Remainder
Problem: 567 ÷ 8
Solution:
- 8 goes into 56 seven times (7 × 8 = 56), write 7 above
- Subtract: 56 - 56 = 0, bring down 7 to make 7
- 8 goes into 7 zero times, write 0 above
- Remainder is 7
Answer: 567 ÷ 8 = 70 remainder 7 (or 70.875 as decimal)
Example 3: Large Number Division
Problem: 9876 ÷ 23
Solution:
- 23 goes into 98 four times (4 × 23 = 92), write 4 above
- Subtract: 98 - 92 = 6, bring down 7 to make 67
- 23 goes into 67 twice (2 × 23 = 46), write 2 above
- Subtract: 67 - 46 = 21, bring down 6 to make 216
- 23 goes into 216 nine times (9 × 23 = 207), write 9 above
- Subtract: 216 - 207 = 9
Answer: 9876 ÷ 23 = 429 remainder 9
Frequently Asked Questions (FAQ)
What is long division?
Long division is a method for dividing one number by another, breaking down the calculation into a series of easy steps. It's particularly useful for dividing large numbers and shows the complete working process including remainders.
How do you do long division step by step?
Follow these steps: 1) Divide the first digit(s) of the dividend by the divisor. 2) Write the quotient above the division symbol. 3) Multiply the quotient by the divisor and write below. 4) Subtract to find the remainder. 5) Bring down the next digit. 6) Repeat until all digits are used.
What is the dividend and divisor in long division?
The dividend is the number being divided (the larger number inside the division bracket). The divisor is the number you're dividing by (the number outside the bracket). For example, in 100 ÷ 5, 100 is the dividend and 5 is the divisor.
What is a remainder in division?
A remainder is the amount left over after division when the dividend doesn't divide evenly by the divisor. For example, 17 ÷ 5 = 3 remainder 2, because 5 goes into 17 three times (15) with 2 left over.
Can this calculator handle decimal numbers?
Yes! Our calculator can handle decimal numbers in both the dividend and divisor. You can also choose to display results as decimals instead of remainders by enabling the "Show decimal result" option.
How do you convert a remainder to a decimal?
To convert a remainder to a decimal, continue the division process by adding a decimal point and zeros to the dividend. For example, 7 ÷ 4 = 1 R3 can be continued as 1.75 by treating the remainder 3 as 3.00 and continuing division.
Why is long division important?
Long division is important because it: 1) Helps understand how division works, 2) Develops problem-solving skills, 3) Is essential for algebra and higher mathematics, 4) Allows you to divide without a calculator, and 5) Shows the complete working process for verification.
Can you divide by zero?
No, division by zero is undefined in mathematics. It's impossible to divide any number by zero because there's no number that, when multiplied by zero, gives you the dividend. Our calculator will show an error if you try to divide by zero.
What's the difference between long division and short division?
Long division shows all steps written out completely, making it easier to follow and learn. Short division is a quicker method where some steps are done mentally, typically used with single-digit divisors. Long division works for any size numbers.
Is this calculator free to use?
Yes! This long division calculator is completely free to use with no registration required. You can perform unlimited calculations and access all features including step-by-step solutions and calculation history.
Can I use this calculator for homework?
Yes, but we recommend using it as a learning tool. Use the step-by-step feature to understand how long division works, then try to solve problems on your own. It's great for checking your answers and learning from mistakes.
Does this work on mobile devices?
Absolutely! Our calculator is fully responsive and works perfectly on smartphones, tablets, and desktop computers. The interface adapts to your screen size for the best experience on any device.
What is chain division and how does it work?
Chain division (or continuous division) is dividing a number by multiple divisors in sequence. For example: 1000 ÷ 5 ÷ 4 ÷ 10 means divide 1000 by 5 (=200), then divide 200 by 4 (=50), then divide 50 by 10 (=5). Our calculator supports both standard division (A÷B) and chain division (A÷B÷C÷D...) with detailed step-by-step solutions for each division in the chain.
Can I divide by more than one number at once?
Yes! Switch to "Chain Division" mode and enter multiple divisors separated by commas or spaces. The calculator will divide your starting number by each divisor in sequence and show you each step. This is useful for complex calculations or when you need to divide repeatedly.
Long Division Tips and Tricks
Memorize Multiplication Tables
Knowing your times tables makes long division much faster. You'll quickly identify how many times the divisor fits into each part of the dividend.
Estimate First
Before starting, estimate the answer by rounding. This helps you catch errors and know if your answer makes sense.
Check Your Work
Multiply your quotient by the divisor and add the remainder. This should equal your original dividend.
Practice Regularly
Like any skill, long division gets easier with practice. Try a few problems each day to build confidence and speed.