About the Long Division Calculator
This long division calculator works a division problem exactly the way it is taught in school: bring down a digit, see how many times the divisor fits, multiply, subtract, and repeat. Every step is listed in a table so students can check homework line by line and parents can follow along without re-learning the method.
You get the answer in every common form — quotient with remainder (176 R 2), a mixed number (176 2/7), the decimal to as many places as you like, and the exact repeating pattern when the decimal never ends, written with the repeating block in parentheses such as 0.(142857).
Enter whole numbers for the dividend (the number being divided) and the divisor (the number you divide by). Negative numbers are handled by dividing the sizes and applying the sign at the end, and the remainder is always reported as a positive amount. That means −1234 ÷ 7 is shown as −176 R 2, read as −(176 R 2) = −176 2/7. With a negative dividend the check Dividend = Divisor × Quotient + Remainder holds for the sizes (1234 = 7 × 176 + 2), not for the signed values; the Euclidean convention would instead write −1234 = 7 × (−177) + 5.
How to use the long division calculator
- 1Enter the dividend — the number you want to divide.
- 2Enter the divisor — the number you are dividing by.
- 3Choose how many decimal places you want in the decimal answer.
- 4Read the quotient and remainder, then follow the step table line by line.
- 5Use the repeating-decimal and mixed-number forms if your homework asks for them.
Formula and method
Long division repeats four moves — divide, multiply, subtract, bring down — one digit at a time from left to right. At each step you ask how many whole times the divisor fits into the current number, write that digit in the quotient, subtract the product, and bring down the next digit.
When the digits run out, whatever is left is the remainder. To continue into decimals, append zeros and keep dividing. Because only a limited number of different remainders are possible, the decimal either ends or starts repeating; the calculator detects the first repeated remainder to show the exact repeating block.
- Dividend
- The number being divided
- Divisor
- The number you divide by (not zero)
- Quotient
- How many whole times the divisor fits
- Remainder
- What is left over, always smaller than the divisor
Worked examples
1,234 ÷ 7
7 goes into 12 once (remainder 5), into 53 seven times (remainder 4), and into 44 six times (remainder 2). So 1234 ÷ 7 = 176 R 2, which is 176 2/7 or 176.285714… with the block 285714 repeating.
9,876 ÷ 12 (no remainder)
12 fits into 98 eight times (96, remainder 2), into 27 twice (24, remainder 3) and into 36 three times exactly. The division comes out even: 823.
5 ÷ 8 (terminating decimal)
8 does not fit into 5, so the quotient is 0 remainder 5. Adding zeros: 50 ÷ 8 = 6 r 2, 20 ÷ 8 = 2 r 4, 40 ÷ 8 = 5 r 0, so 5/8 = 0.625 exactly.
−1,234 ÷ 7 (negative dividend)
Divide the sizes, 1234 ÷ 7 = 176 R 2, then apply the minus sign: −176 R 2, meaning −(176 2/7) ≈ −176.285714. The identity holds for the sizes (7 × 176 + 2 = 1234); the Euclidean form with a non-negative remainder is −1234 = 7 × (−177) + 5.
Frequently asked questions
How do you do long division step by step?+
Divide the first digit(s) by the divisor, write the whole-number answer on top, multiply it back by the divisor, subtract, then bring down the next digit. Repeat until no digits remain; what is left is the remainder.
How do I write a remainder as a fraction or decimal?+
Put the remainder over the divisor: 176 R 2 when dividing by 7 becomes 176 2/7. For a decimal, keep dividing by adding zeros after the decimal point, which gives 176.285714…
How do I know if a decimal will repeat?+
After simplifying the fraction, if the denominator has only 2 and 5 as prime factors the decimal terminates. Any other prime factor (3, 7, 11…) makes it repeat, and the repeating block is at most one digit shorter than the denominator.
How do I check my long division answer?+
Multiply the quotient by the divisor and add the remainder. If you get the original dividend back, the answer is correct — for example 7 × 176 + 2 = 1234.
What happens with negative numbers?+
Divide the absolute values, then make the quotient negative if exactly one of the numbers is negative. This calculator reports the remainder as a positive amount alongside that signed quotient, so −1234 ÷ 7 = −176 R 2 means −(7 × 176 + 2). In the Euclidean convention, where Dividend = Divisor × Quotient + Remainder must hold exactly, it is −177 R 5 instead.