Long Division Calculator

The long division algorithm represents a systematic approach to division, breaking down complex calculations into manageable steps. Understanding the theoretical foundations helps in mastering this fundamental mathematical operation:

The long division process follows a structured sequence of steps. Each step builds on previous operations to arrive at the final result:

Example: 789 ÷ 4. You start with 7 (4 goes into 7 one time), subtract 4 to get a remainder of 3, then bring down the next digit 8 to form 38. Next, 4 goes into 38 nine times (9 × 4 = 36), subtract to get remainder 2, then bring down 9 to form 29. Finally, 4 goes into 29 seven times (7 × 4 = 28), leaving remainder 1. The integer result is 197 remainder 1.

If you continue, the remainder can be used to form decimal digits by repeatedly bringing down zeros. This calculator shows a short decimal expansion when the remainder is not zero.

A remainder means the division does not end cleanly as an integer. The exact value can be written as: quotient + (remainder ÷ divisor). For example, 197 remainder 1 equals 197 + 1/4 = 197.25.

Some fractions create repeating decimals. In long division, repetition happens because the remainder can only take a limited set of values (0 through divisor - 1). If the same remainder appears again, the digits will repeat from that point onward. This tool limits the displayed decimal expansion to keep the steps readable.

Long division principles extend across different number systems and types. Understanding these applications broadens mathematical comprehension:

Understanding common errors and their sources helps in developing accurate division skills. Regular patterns emerge in division mistakes:

Long division serves as a foundational skill in mathematics education. Its mastery supports understanding of more advanced concepts:

These educational applications demonstrate the continuing importance of mastering long division in mathematical development.