➗ Long Division Calculator
By ToolNimba Education Team · Updated 2026-06-19
Enter a dividend and a divisor to see the answer and the working.
This long division calculator divides one whole number by another and shows the full working, not just the answer. Enter the dividend (the number being divided) and the divisor (the number you divide by), and you get the quotient, the remainder, and the decimal result. Below that, each bring-down step is laid out exactly the way long division is taught at school, so you can follow how the answer is reached and check your own work.
What is the Long Division Calculator?
Long division is a written method for dividing larger numbers that a single mental step cannot handle. Instead of dividing the whole number at once, you work through it one digit at a time, from left to right. At each stage you ask how many times the divisor fits into the running number, write that digit in the quotient, subtract what it accounts for, and bring down the next digit. Repeating this until there are no digits left gives the quotient, and whatever is left over is the remainder.
Every division can be described by one identity: dividend = divisor x quotient + remainder, where the remainder is always smaller than the divisor. For example, 1234 divided by 7 gives a quotient of 176 and a remainder of 2, and indeed 7 x 176 + 2 = 1234. The remainder is the part that does not divide evenly. If you want a single number instead of a quotient-and-remainder pair, you continue dividing past the decimal point, which is how 1234 divided by 7 becomes about 176.2857.
The quotient is the count of whole groups, and the remainder is what is left when no more whole groups can be formed. A remainder of zero means the divisor divides the dividend exactly (the dividend is a multiple of the divisor). Dividing by zero, by contrast, has no answer at all: there is no number of zero-sized groups that adds up to a positive quantity, so division by zero is left undefined rather than given a value.
When to use it
- Helping a student check long-division homework and see exactly where a step went wrong.
- Working out a quotient and remainder by hand when a plain calculator only shows the decimal.
- Splitting a total into equal whole groups and seeing how many items are left over.
- Converting a fraction to a decimal by continuing the division past the decimal point.
How to use the Long Division Calculator
- Enter the dividend, the number you want to divide.
- Enter the divisor, the number you are dividing by (it cannot be zero).
- Read off the quotient, the remainder and the decimal result at the top.
- Scroll to the step-by-step working to see each bring-down and subtraction.
Formula & method
Worked examples
Divide 1234 by 7 using long division.
- 7 goes into 1 zero times, so combine: 7 goes into 12 once (1 x 7 = 7), leaving 5.
- Bring down the 3 to make 53. 7 goes into 53 seven times (7 x 7 = 49), leaving 4.
- Bring down the 4 to make 44. 7 goes into 44 six times (6 x 7 = 42), leaving 2.
- No digits remain. Quotient = 176, remainder = 2.
- Check: 7 x 176 + 2 = 1232 + 2 = 1234.
Result: Quotient 176, remainder 2, decimal about 176.2857
Divide 952 by 4 (an exact division).
- 4 goes into 9 two times (2 x 4 = 8), leaving 1.
- Bring down the 5 to make 15. 4 goes into 15 three times (3 x 4 = 12), leaving 3.
- Bring down the 2 to make 32. 4 goes into 32 eight times (8 x 4 = 32), leaving 0.
- No digits remain. Quotient = 238, remainder = 0.
- Check: 4 x 238 + 0 = 952.
Result: Quotient 238, remainder 0, decimal exactly 238
Example divisions showing quotient, remainder and decimal
| Dividend | Divisor | Quotient | Remainder | Decimal |
|---|---|---|---|---|
| 1234 | 7 | 176 | 2 | 176.2857 |
| 952 | 4 | 238 | 0 | 238 |
| 100 | 3 | 33 | 1 | 33.3333 |
| 4567 | 12 | 380 | 7 | 380.5833 |
| 45 | 9 | 5 | 0 | 5 |
Key parts of a division and what they mean
| Part | Meaning |
|---|---|
| Dividend | The number being divided |
| Divisor | The number you divide by |
| Quotient | How many whole groups fit |
| Remainder | What is left over (smaller than the divisor) |
Common mistakes to avoid
- Forgetting to bring down every digit. Each digit of the dividend must be brought down in turn, even when the divisor goes into the current number zero times. Skipping a digit, or skipping the zero it produces in the quotient, shifts every later digit and gives a wrong answer.
- Letting the remainder be larger than the divisor. A valid remainder is always smaller than the divisor. If your leftover is as big as the divisor or bigger, the quotient digit was too small, so increase it and subtract again.
- Confusing the dividend and the divisor. The dividend is the number being split up and the divisor is the number of parts. Swapping them, for example dividing 7 by 1234 instead of 1234 by 7, gives a completely different result.
- Trying to divide by zero. Division by zero has no answer because no number of zero-sized groups can make a positive total. The calculator flags this rather than returning a value.
Glossary
- Dividend
- The number that is being divided up.
- Divisor
- The number you are dividing the dividend by.
- Quotient
- The whole-number result of the division, the count of complete groups.
- Remainder
- The amount left over after taking out as many whole groups as possible, always smaller than the divisor.
- Bring down
- The step of carrying the next digit of the dividend into the running calculation.
- Decimal result
- The single-number answer obtained by continuing the division past the decimal point.
Frequently asked questions
What is long division?
Long division is a written method for dividing larger numbers one digit at a time. You repeatedly see how many times the divisor fits into the running number, write that digit in the quotient, subtract, and bring down the next digit until none remain. The result is a quotient and a remainder.
What is the difference between the quotient and the remainder?
The quotient is how many whole groups of the divisor fit into the dividend, and the remainder is what is left over once no more whole groups can be formed. The remainder is always smaller than the divisor. For 1234 divided by 7 the quotient is 176 and the remainder is 2.
How do I write a division with a remainder?
You can write it as "quotient remainder r", for example 176 r2, or use the identity dividend = divisor x quotient + remainder. To get a single number instead, continue dividing past the decimal point to find the decimal result.
Why can you not divide by zero?
Dividing asks how many groups of the divisor make up the dividend. With a divisor of zero, no number of zero-sized groups can ever add up to a positive amount, so there is no sensible answer. Mathematicians leave division by zero undefined, and this tool flags it instead of returning a value.
How do I check my long division answer?
Multiply the quotient by the divisor and add the remainder. If you get back the original dividend, the answer is correct. For example, 7 x 176 + 2 = 1234, which confirms 1234 divided by 7 is 176 remainder 2.
Can this calculator show decimals as well as remainders?
Yes. It gives the integer quotient and remainder, and separately the decimal result. For example 100 divided by 3 shows a quotient of 33 with remainder 1, and a decimal result of about 33.3333.