Long Division Calculator: Divide with Step-by-Step Working
Free long division calculator: enter dividend and divisor to get the quotient and remainder with full step-by-step long division working shown.
What long division does
Long division is the written method for dividing one whole number by another when the answer is not obvious at a glance. The number being divided is called the dividend, and the number you divide by is called the divisor. The result has two parts: the quotient (how many whole times the divisor fits) and the remainder (what is left over). For example, 154 ÷ 5 gives a quotient of 30 and a remainder of 4, because 5 fits into 154 thirty times (5 × 30 = 150) with 4 left over.
This calculator performs the full long division algorithm and shows every bring-down step, exactly as you would write it on paper. It accepts positive and negative integers. The divisor cannot be zero, since division by zero is undefined in mathematics. Every result is computed directly by the calculation engine in your browser, nothing is estimated or generated, and the final step always includes a check: quotient × divisor + remainder must equal the dividend.
How to use the long division calculator
Enter the dividend in the first box. This is the larger number in most everyday problems, the total you are splitting up, for instance 1,000 when dividing prize money, or 365 when working out weeks in a year. Enter the divisor in the second box, the size of each group or the number of groups, then press Calculate.
The calculator works through the digits of the dividend from left to right. At each step it asks: how many whole times does the divisor fit into the current working number? It multiplies, subtracts, and brings down the next digit, repeating until no digits remain. The step panel lists each of these mini-divisions so you can follow along or copy the working into your homework.
If you enter a negative dividend or divisor, the calculator works with the positive values and applies the sign to the quotient at the end, which matches the standard convention: the quotient is negative when exactly one of the two numbers is negative, and the remainder takes the sign of the dividend.
The long division method, step by step
The method is a loop of four actions, remembered by many students as divide, multiply, subtract, bring down:
- Divide: look at the leftmost digit (or digits) of the dividend that form a number at least as big as the divisor. Ask how many whole times the divisor fits.
- Multiply: multiply the divisor by that digit and write the product under the working number.
- Subtract: subtract to find what is left. This leftover must be smaller than the divisor, otherwise the digit chosen in step 1 was too small.
- Bring down: bring down the next digit of the dividend next to the leftover and repeat from step 1.
When every digit has been brought down, the digits collected in step 1 form the quotient and the final leftover is the remainder. The golden rule connecting them is: dividend = divisor × quotient + remainder, with the remainder always smaller than the divisor. The calculator verifies this identity on every single computation.
Example: 154 ÷ 5
Step 1: 5 goes into 1 zero times. Bring down the 5 to make 15. 15 ÷ 5 = 3, since 3 × 5 = 15, remainder 0.
Step 2: Bring down the 4 to make 4. 4 ÷ 5 = 0, since 5 does not fit into 4 at all, remainder 4.
Result: quotient 30, remainder 4.
Check: 30 × 5 + 4 = 150 + 4 = 154. Correct.
More examples: 100 ÷ 7 = 14 remainder 2; 1,000 ÷ 8 = 125 remainder 0; 365 ÷ 7 = 52 remainder 1 (52 weeks and 1 day).
Common mistakes
- Forgetting the zero in the quotient: when the divisor does not fit into the working number (like 4 ÷ 5 above), the quotient digit is 0, and skipping it gives a wrong, shorter answer.
- Bringing down two digits at once: only one digit comes down per step. If the working number is still smaller than the divisor after bringing one digit down, write 0 in the quotient and bring down another.
- Remainder larger than the divisor: if your subtraction leaves something as big as the divisor, the quotient digit was too small, go back and increase it.
- Losing track of place value: each quotient digit sits above the digit just brought down. Misalignment is the most common source of wrong answers on paper.
When long division is useful
Long division shows up constantly outside the classroom. Splitting a restaurant bill evenly, working out how many full packs you can make from bulk items, converting total days into weeks, or checking whether a number divides evenly (a remainder of zero means it is a factor) all use the same idea. It is also the foundation for polynomial long division in algebra and for the division algorithm used in computer arithmetic. If you only need a quick decimal answer, the universal solver handles that, but when you need the quotient and remainder separately, or you want to see the working, this is the right tool.
The quotient is the whole number of times the divisor fits into the dividend; the remainder is what is left over. In 154 ÷ 5, the quotient is 30 and the remainder is 4. They are linked by the rule: dividend = divisor × quotient + remainder.
Division asks “how many groups of this size fit?” and no number of zero-sized groups can make a nonzero total. In symbols, if a ÷ 0 = q, then a = 0 × q = 0, which is impossible when a is not zero. So division by zero is left undefined, and the calculator rejects it.
The division is performed on the absolute values, then the quotient takes a negative sign if exactly one input was negative (−154 ÷ 5 = −30 remainder −4). The remainder always carries the sign of the dividend, which keeps the identity dividend = divisor × quotient + remainder true.
It means the division is exact: the divisor is a factor of the dividend. For example, 1,000 ÷ 8 = 125 remainder 0, so 8 divides 1,000 evenly. A zero remainder is also how divisibility tests work.