Calcly.xyz

Long Division Calculator

Perform long division with step-by-step solutions. Learn the traditional long division method with detailed explanations and visual representation of each step.

Division Input

÷

Division Result

125 ÷ 7
17
Remainder: 6
As Mixed Number:
17 6/7
As Decimal:
17.8571
As Fraction:
125/7
Verification:
17 × 7 + 6 = 125
Division Type:
Division with remainder
Decimal Type:
Non-repeating

Step-by-Step Long Division

1
Perform integer division
125 ÷ 7 = 17 remainder 6
7 goes into 125 exactly 17 times with 6 left over
2
Calculate decimal place 1
60 ÷ 7 = 8 remainder 4
Bring down 0 to make 60, then divide by 7
3
Calculate decimal place 2
40 ÷ 7 = 5 remainder 5
Bring down 0 to make 40, then divide by 7
4
Calculate decimal place 3
50 ÷ 7 = 7 remainder 1
Bring down 0 to make 50, then divide by 7
5
Calculate decimal place 4
10 ÷ 7 = 1 remainder 3
Bring down 0 to make 10, then divide by 7

How to Use This Calculator

1
Enter the Dividend
Input the number you want to divide (the larger number in most cases).
2
Enter the Divisor
Input the number you're dividing by. This cannot be zero.
3
Choose Decimal Precision
Select how many decimal places you want for the result (if applicable).
4
View Results
See the quotient, remainder, and different representations of the result.

Understanding Long Division

What is Long Division?

Long division is a method for dividing large numbers by breaking the process into smaller, manageable steps. It's called "long" because it involves a longer process than simple division, but it allows us to divide any numbers systematically.

The Long Division Process

1. Divide
Look at the leftmost digits of the dividend and see how many times the divisor goes into it.
2. Multiply
Multiply the divisor by the quotient digit and write the result below.
3. Subtract
Subtract the multiplication result from the current dividend portion.
4. Bring Down
Bring down the next digit from the dividend and repeat the process.

Key Terms

Dividend
The number being divided (inside the division symbol).
Divisor
The number you're dividing by (outside the division symbol).
Quotient
The result of the division (above the division symbol).
Remainder
What's left over when the division doesn't result in a whole number.

Example Calculations

Example 1: Simple Division

Problem: 84 ÷ 4
Step 1: 8 ÷ 4 = 2 (write 2 above the 8)
Step 2: 4 ÷ 4 = 1 (write 1 above the 4)
Result: 21 with no remainder

Example 2: Division with Remainder

Problem: 125 ÷ 7
Step 1: 12 ÷ 7 = 1 remainder 5
Step 2: Bring down 5 → 55
Step 3: 55 ÷ 7 = 7 remainder 6
Result: 17 remainder 6, or 17⁶⁄₇

Example 3: Decimal Result

Problem: 22 ÷ 7 (to 4 decimal places)
Step 1: 22 ÷ 7 = 3 remainder 1
Step 2: Add decimal point, continue with 10 ÷ 7 = 1 remainder 3
Step 3: 30 ÷ 7 = 4 remainder 2
Step 4: 20 ÷ 7 = 2 remainder 6
Step 5: 60 ÷ 7 = 8 remainder 4
Result: 3.1428...

Frequently Asked Questions

When should I use long division instead of a calculator?

Long division is useful for understanding the division process, checking calculator results, working with exact fractions, and in situations where calculators aren't available. It's also required in many educational settings.

What if the division never ends (repeating decimals)?

Some divisions result in repeating decimals (like 1/3 = 0.333...). The calculator will show the pattern and indicate when decimals repeat. You can choose how many decimal places to calculate.

How do I check if my long division is correct?

Multiply the quotient by the divisor and add the remainder. The result should equal the original dividend. For example: if 125 ÷ 7 = 17 remainder 6, then 17 × 7 + 6 = 119 + 6 = 125 ✓

Can I divide by decimal numbers?

This calculator focuses on integer division (whole numbers). For decimal division, you can multiply both numbers by 10, 100, etc., to make them whole numbers, then divide.

Related Calculators

Basic Calculator
Simple arithmetic operations
Fraction Calculator
Calculate with fractions
Percentage Calculator
Calculate percentages
GCF Calculator
Greatest Common Factor
LCM Calculator
Least Common Multiple
Scientific Calculator
Advanced mathematical functions