Long Division Calculator

About the Long Division Calculator

Long division is the algorithmic process for dividing numbers of any size, producing a quotient and remainder. Despite calculators making it less necessary in everyday life, understanding long division builds arithmetic intuition and is still taught in schools worldwide as a foundation for polynomial division and other advanced mathematics. Our step-by-step long division calculator shows every intermediate step so you can follow or teach the process.

How It Works

The algorithm: (1) Divide the first digit(s) of the dividend by the divisor to get the first digit of the quotient. (2) Multiply that digit by the divisor. (3) Subtract from the current portion of the dividend. (4) Bring down the next digit. (5) Repeat until no digits remain. (6) The final subtracted value is the remainder. Example: 256 ÷ 8. 25 ÷ 8 = 3 remainder 1. Bring down 6 → 16 ÷ 8 = 2. Quotient = 32, remainder = 0.

Tips & Best Practices

• ✓Verify by multiplication: quotient × divisor + remainder should equal the original dividend.
• ✓In programming, integer division (/) gives quotient; modulo (%) gives remainder.
• ✓Decimal long division: continue bringing down zeros after the decimal point.
• ✓Polynomial long division uses the same algorithm as numerical long division.
• ✓Long division algorithm efficiency: O(n) where n = number of digits in dividend.

Who Uses This Calculator

Primary and middle school students learning division, parents helping with homework, teachers creating worked examples, students transitioning to polynomial division in algebra, and developers debugging integer arithmetic edge cases all benefit from step-by-step long division.