Home ›
Math › Long Division Calculator
· 🌐 EN / DE Long Division Calculator
Divide one integer by another and see the quotient, remainder, decimal value, and every step of the long-division process.
Example
Divide 127 by 4:
127 / 4
12 / 4 = 3, remainder 0 -> 12 - 12 = 0
07 / 4 = 1, remainder 3 -> 7 - 4 = 3
Quotient = 31, Remainder = 3
Decimal = 31.75 (check: 31 x 4 + 3 = 127)
How it works
Enter a dividend and a divisor, both whole numbers. The tool computes the quotient and remainder, the decimal result, and lays out the long-division steps digit by digit.
Good to know
The Long Division Calculator takes a dividend and a divisor (both whole numbers) and returns the quotient, the remainder, the exact decimal value, and a digit-by-digit breakdown of the long-division process. It's built for students learning the algorithm, parents and tutors checking homework, and anyone who needs to see the working rather than just a final answer.
Reach for it when a plain calculator's decimal output isn't what you need. If you want the integer quotient plus a leftover remainder (for example, splitting 127 items into groups of 4), the headline reads as "31 R 3", with the separate Quotient, Remainder, and Decimal fields giving each form at a glance. The step table mirrors what you'd write on paper: which digit is brought down, the current working value, the quotient digit chosen, the subtraction, and the running remainder.
A few things to keep in mind when reading the result:
- Negative inputs use truncated division, so the quotient rounds toward zero and the remainder takes the sign of the dividend; the step table works on the absolute values and the sign is applied to the final answer.
- The Decimal field trims trailing zeros, so 127 / 4 shows 31.75 exactly, while a result like 1 / 3 is shown rounded to ten decimal places rather than as a repeating decimal.
The tool always prints a "Check" line (quotient x divisor + remainder = dividend) so you can confirm the result reconstructs the original number. Note that it only accepts whole numbers; if you need to divide fractions or non-integers, use a fraction calculator instead, and remember the divisor can never be zero, which returns "undefined".
Frequently asked questions
How is the remainder calculated for negative numbers?
This tool uses truncated division: the quotient is rounded toward zero and the remainder takes the sign of the dividend. For example, -127 / 4 gives quotient -31 and remainder -3, since -31 x 4 + (-3) = -127.
Why does the step table only use the absolute values?
Long division is performed on the magnitudes of the numbers, then the sign is applied to the final quotient and remainder. This keeps the digit-by-digit working clear, and the result fields show the correctly signed answer.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the difference between the quotient and the remainder?
The quotient is how many whole times the divisor fits into the dividend, and the remainder is what is left over that is too small to divide again. For 127 divided by 4, the quotient is 31 and the remainder is 3 because 31 times 4 is 124, leaving 3.
How do you do long division step by step?
You divide the leftmost digits of the dividend by the divisor, write the quotient digit, multiply it back, subtract, then bring down the next digit and repeat until no digits remain. The leftover after the last step is the remainder, which this calculator shows in its step table.
What is 127 divided by 4?
127 divided by 4 equals 31 with a remainder of 3, or 31.75 as a decimal. You can verify it because 31 times 4 plus 3 equals 127.
How do you write a remainder as a decimal?
Divide the remainder by the divisor and add it to the quotient. A remainder of 3 over a divisor of 4 is 0.75, so 31 remainder 3 becomes 31.75.
Why is dividing by zero undefined?
There is no number that, when multiplied by zero, produces a non-zero dividend, so the result has no meaningful value. This calculator returns undefined and asks for a non-zero divisor.
What is the dividend and divisor in a division problem?
The dividend is the number being divided (the total amount) and the divisor is the number you divide by (the size of each group). In 127 divided by 4, 127 is the dividend and 4 is the divisor.
Can long division give a repeating decimal?
Yes, when the divisor does not divide the dividend evenly into a terminating decimal, such as 1 divided by 3 giving 0.3333... This tool displays such results rounded to ten decimal places rather than as a repeating pattern.
Related calculators