Solve any division problem with a complete step-by-step solution showing quotient, remainder, and decimal result.
Enter the dividend and divisor to see the full long division process.
Long division is a standard mathematical procedure for dividing large numbers that breaks the problem into a series of simpler steps. It's one of the most important arithmetic skills taught in elementary school, typically introduced in 3rd or 4th grade. The process involves dividing, multiplying, subtracting, and bringing down digits — repeated until the problem is fully solved.
Unlike simple division that can be done mentally, long division provides a structured framework for handling numbers of any size. The method is explained extensively by Khan Academy's arithmetic course, and is a foundational skill recognized by the National Council of Teachers of Mathematics (NCTM).
Long division follows a repeating cycle of four operations, often remembered by the mnemonic DMSB: Divide, Multiply, Subtract, Bring down.
Example: 845 ÷ 3
Step 1: 8 ÷ 3 = 2 (write 2 above), 2 × 3 = 6, 8 - 6 = 2
Step 2: Bring down 4 → 24, 24 ÷ 3 = 8 (write 8 above), 8 × 3 = 24, 24 - 24 = 0
Step 3: Bring down 5 → 5, 5 ÷ 3 = 1 (write 1 above), 1 × 3 = 3, 5 - 3 = 2
Answer: 845 ÷ 3 = 281 remainder 2 (or 281.667)
Understanding these terms is essential for algebra and higher mathematics. For related concepts, check our Fraction Calculator to convert remainders into fractions, or our Average Calculator which uses division as its core operation.
When a division doesn't come out evenly, you can continue the long division process by adding decimal places. Simply add a decimal point to the quotient and zeros to the remainder, then continue dividing. This process can result in terminating decimals (like 1/4 = 0.25) or repeating decimals (like 1/3 = 0.333...). For a deeper understanding, Math is Fun offers excellent visual guides.
No, division by zero is undefined in mathematics. There is no number that, when multiplied by zero, gives a non-zero result. Attempting to divide by zero on a calculator will produce an error.
Multiply the quotient by the divisor, then add the remainder. The result should equal the dividend. For example: 281 × 3 + 2 = 843 + 2 = 845 ✓
The remainder is the whole number left over after division. The decimal representation continues dividing to show the fractional part. For 7 ÷ 2: the remainder is 1, while the decimal is 3.5.
The modern long division algorithm was developed in the late Middle Ages. The method as we know it today was popularized by Henry Briggs around 1600, though ancient civilizations had their own division methods.