Long Division Calculator
Long division is a step-by-step method for dividing large numbers by hand. It breaks the division into a sequence of smaller operations — divide, multiply, subtract, bring down — repeated until the calculation is complete. The result is a quotient and (optionally) a remainder.
Tip: Estimate the quotient digit first: if dividing 487 by 32, ask "how many times does 32 fit into 48?" — approximately 1. Then check by multiplying.
- 1Write the dividend inside the bracket and the divisor outside
- 2Divide the first digit(s) of the dividend by the divisor to get the first quotient digit
- 3Multiply that quotient digit by the divisor and write the product below
- 4Subtract to find the remainder, then bring down the next digit
- 5Repeat steps 2–4 until all digits are processed
Division by zero
Division by zero is undefined. Any number divided by zero has no meaningful answer in standard arithmetic.
Expressing the remainder
The remainder can be written as R7, as a fraction (7/32), or as a decimal (0.21875). All three forms are valid.
| Term | Definition | Example (487 ÷ 32 = 15 R 7) |
|---|---|---|
| Dividend | The number being divided | 487 |
| Divisor | The number you divide by | 32 |
| Quotient | The result of the division | 15 |
| Remainder | What is left over | 7 |
Fun Fact
Long division was popularized in Europe in the 15th century by Fibonacci's Liber Abaci. Before it, division was done with more complex methods using lattices or counting boards.