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.
Long division is a step-by-step method for dividing large numbers by hand, breaking one difficult division into a series of simple ones. It works through the dividend digit by digit using a four-step cycle: divide, multiply, subtract, bring down. The method makes the structure of division visible, which is why it remains part of the curriculum despite the existence of calculators.
| Term | Meaning | In 847 / 7 |
|---|---|---|
| Dividend | The number being divided | 847 |
| Divisor | The number you divide by | 7 |
| Quotient | The answer | 121 |
| Remainder | What is left over | 0 |
Cycle 1: the first digit
Cycle 2
Cycle 3
847 divided by 7 is 121 with no remainder
Three ways to express the answer
All three are correct; which you use depends on the context
Divide, Multiply, Subtract, Bring down. Many teachers use "Does McDonald's Sell Cheeseburgers" to fix the sequence. Almost every long division mistake comes from skipping the subtract step or forgetting to bring down the next digit.
When the divisor contains a decimal, shift it to become a whole number and shift the dividend by the same number of places. This works because multiplying both numbers by the same power of ten leaves the quotient unchanged.
The answer is 13
The obvious objection is that calculators exist. The counter-argument is that long division teaches place value, estimation and the structure of division in a way that reading a display does not. A student who understands the algorithm can spot when an answer is implausible.
It also generalises. Polynomial long division in algebra follows the same four-step cycle with algebraic terms instead of digits, and students who never internalised the numeric version tend to struggle with it.
Rounding to check is the fastest error catch available. Dividing 847 by 7, note that 7 times 120 is 840, so the answer should be just over 120. Getting 121 confirms it; getting 12 or 1,210 would immediately flag a place value error.
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