Long Division Calculator
Perform long division with step-by-step walkthrough showing each bring-down, multiply, and subtract step.
About Long Division
Long division is a method for dividing large numbers by breaking the problem into a sequence of simpler steps. It is the standard algorithm taught in schools for integer division and forms the foundation for understanding polynomial division and other advanced mathematical concepts.
The Algorithm
The long division algorithm works digit by digit from left to right. At each step: (1) bring down the next digit of the dividend, (2) determine how many times the divisor goes into the current number (the quotient digit), (3) multiply the divisor by that digit, (4) subtract to get the remainder, and (5) repeat. The final remainder is the overall remainder.
Quotient and Remainder
For integers a ÷ b, the result is expressed as a = b × q + r, where q is the quotient and 0 ≤ r < |b| is the remainder. When the remainder is not zero, the division can be continued as a decimal by treating the remainder as a new dividend (appending zeros). The decimal form is simply the true division result.
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For a related calculation, use Big Number Calculator to add, subtract, and multiply arbitrarily large integers using JavaScript BigInt. Perfect for 100+ digit numbers. Alternatively, use Average Calculator to calculate mean, median, mode, range, min, max, sum, and count from a list of numbers.