Long Division Calculator
Perform long division with step-by-step working shown for better understanding.
Understanding Long Division
Long division is a step-by-step method for dividing large numbers, showing the work as you calculate the quotient and remainder. It's an essential skill in mathematics education and a foundation for understanding more complex mathematical concepts.
How Long Division Works:
- The divisor is the number you're dividing by
- The dividend is the number being divided
- The quotient is the result of the division
- The remainder is the amount left over when the division cannot be done evenly
Long Division Process:
- Divide the first digit(s) of the dividend by the divisor
- Multiply the result by the divisor and write it under the corresponding digits of the dividend
- Subtract and bring down the next digit from the dividend
- Repeat the process until all digits have been used
- Any remaining value becomes the remainder
Example of Long Division:
Example 1: 725 ÷ 5
_145
5 )725
5
_22
20
_25
25
0
Result: 145 with no remainder
Example 2: 1234 ÷ 56
_22r2
56 )1234
112
_114
112
2
Result: 22 with remainder 2
Applications of Long Division:
In Mathematics:
- Converting fractions to decimals
- Performing polynomial division
- Computing modular arithmetic
- Finding recurring decimals
Educational Benefits:
- Develops systematic problem-solving
- Reinforces place value understanding
- Builds foundational arithmetic skills
- Encourages mathematical reasoning
Advanced Division Concepts
- Polynomial Long Division: Similar to numeric long division but used for dividing polynomials by other polynomials.
- Synthetic Division: A shortcut method for dividing polynomials by linear factors.
- Decimal Long Division: For finding the decimal representation of fractions, including repeating decimals.
- Binary Long Division: Applying long division methods to binary numbers, used in computer science.
How to Use the Calculator:
- Enter the dividend (the number to be divided) in the first field
- Enter the divisor (the number that divides) in the second field
- Click "Calculate Division" to see the result
- View the quotient, remainder, and the complete step-by-step working
- Use the division check to verify the result