Long Division Calculator
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Perform long division with step-by-step breakdown. Shows quotient, remainder, decimal result, and full working.
Enter your values below and click Calculate for instant results.
Long division is a method for dividing larger numbers step by step, working from left to right through the digits of the dividend. Each step involves dividing the current working portion by the divisor, writing the quotient digit, multiplying back to find the product, and subtracting to find the remainder, which carries forward to the next digit.
The key steps in long division: Divide, Multiply, Subtract, Bring down. Repeat for each digit of the dividend. When you have worked through all digits, the final remainder is the remainder of the division problem.
The quotient is the whole number result of the division. The remainder is what is left over. When 23 is divided by 5, the quotient is 4 (because 5 goes into 23 four times) and the remainder is 3 (because 4 times 5 equals 20, leaving 3). This can be written as 23 = 5 times 4 + 3.
Understanding long division builds number sense and a deep understanding of how our base-10 number system works. It is the foundation for understanding polynomial long division in algebra, which uses the exact same procedure applied to expressions rather than numbers. Even with calculators available, understanding the process helps you catch errors and build estimation skills.