Long Division Calculator
Divide any two numbers and see the long division written out, with every step, the remainder and the exact or rounded decimal.
7 fits into 1,234 a total of 176 whole times, leaving 2.
Long division worked out
Read the quotient across the top. Each pair of rows below the dividend is one round of divide, multiply, subtract and bring down.
Your calculation
The same steps the calculator runs, with your numbers.
Multiples of 7 for this division
Long division only ever needs the first nine multiples of the divisor. Writing them out first turns each step into a lookup.
| Multiple | Value | Used in |
|---|
Digits are computed with exact whole number arithmetic, so long inputs have no rounding error. Only the rounded decimal answer is rounded.
What Is Long Division?
Long division is the written method for dividing numbers that are too large to divide in your head. You split the problem into small steps, one digit of the dividend at a time, and write each step under the number. OpenStax Prealgebra describes it as the process to use when the divisor or the dividend has more than one digit.
Four terms describe every division. The dividend is the number being divided, the divisor is the number you divide by, the quotient is the result and the remainder is what is left over when the divisor does not fit exactly. In 1,234 ÷ 7 = 176 R 2, the dividend is 1,234, the divisor is 7, the quotient is 176 and the remainder is 2.
In the written layout the divisor sits to the left of a bracket, the dividend sits under a bar and the quotient is built digit by digit above the bar. Each digit comes from the same four step cycle: divide, multiply, subtract, bring down.
How to Use the Long Division Calculator
- Enter the dividend and the divisor. Whole numbers, decimals and negative numbers all work, for example 8746, 47.25 or −17. Thousands separators such as 1,234 are accepted.
- Choose how to show the answer. Quotient and remainder gives the school answer such as 176 R 2. Rounded decimal keeps dividing to the number of decimal places you choose. Exact decimal with repeats keeps dividing until the remainder reaches 0 or repeats, and marks the repeating digits with a bar.
- Read the results. The answer appears first, then the full long division layout, tiles with the other forms of the answer (mixed number, fraction, decimal and repeating block), the steps in words and a table of the divisor's multiples.
The calculator updates as you type. Press Enter or Calculate to run it, or use a quick example to fill in the numbers. If the divisor has decimals, the layout shows the division after the decimal points have been moved, just as you would write it on paper.
Long Division Steps
Every round of long division follows the same four steps. Here is 1,234 ÷ 7.
Each quotient digit goes directly above the last digit you brought down. Stop when no digits are left, or keep going past the decimal point if you want a decimal answer.
How to Check a Division
Division and multiplication undo each other, so every answer can be checked with the division identity:
If the check fails, look for a subtraction slip or a missing zero in the quotient. If a remainder in any step is as large as the divisor, the quotient digit in that step was one too small.
Long Division with a Two Digit Divisor
With a divisor such as 23, you cannot rely on times tables, so estimate each quotient digit and then adjust. Round the divisor to a friendly number, divide, and test the guess by multiplying.
For 8,746 ÷ 23: 23 does not go into 8, so start with 87. Rounding 23 to 20 suggests 4, but 4 × 23 = 92 is more than 87, so use 3: 3 × 23 = 69 and 87 − 69 = 18. Bring down 4 to make 184. The estimate 9 gives 207, too big, so try 8: 8 × 23 = 184, remainder 0. Bring down 6: 23 does not go into 6, so write 0 in the quotient. The answer is 380 R 6.
A second example, 4,825 ÷ 25, divides exactly. 25 goes into 48 once (remainder 23), into 232 nine times (225, remainder 7) and into 75 three times with nothing left, so 4,825 ÷ 25 = 193. The multiples table in the results lists 1 × 23 through 9 × 23, which removes the guesswork for larger divisors.
Long Division with Decimals
Decimal divisor: move the divisor's decimal point to the right until it is a whole number, and move the dividend's decimal point the same number of places. 47.25 ÷ 3.5 becomes 472.5 ÷ 35. This does not change the answer, because both numbers were multiplied by 10.
Decimal dividend: put the decimal point in the quotient directly above the one in the dividend, then divide as usual. For 12.5 ÷ 4: 12 ÷ 4 = 3, bring down 5 (and place the point), then add zeros: 5, 10, 20 give the digits 1, 2 and 5, so 12.5 ÷ 4 = 3.125.
So 472.5 ÷ 35: 47 gives 1 (remainder 12), 122 gives 3 (remainder 17) and 175 gives 5 exactly, so 47.25 ÷ 3.5 = 13.5. A price example: a 24 bottle case costing $3.99 works out to 3.99 ÷ 24 = 0.16625, or $0.17 per bottle to the nearest cent.
Remainders as Fractions and Decimals
A remainder can be written three ways. As a fraction, put the remainder over the divisor: 1,439 ÷ 4 = 359 R 3 = 359 3/4. As a decimal, keep dividing with zeros added after the decimal point: 359.75. As a whole number answer, round or keep the remainder, depending on the question.
Word problems decide which form makes sense. Sharing 100 dollars among 3 people gives 33.33 dollars each, rounded to cents. Packing 100 eggs into boxes of 12 gives 8 full boxes with 4 eggs left over, so the remainder matters.
When rounding, look at the next digit. 100 ÷ 3 = 33.333…, and the third decimal digit is 3, so it rounds down to 33.33. 1 ÷ 8 = 0.125 rounds up to 0.13 at two places because the next digit is 5.
Repeating Decimals in Long Division
Each remainder is smaller than the divisor, so only a limited set of remainders can occur. When one comes back, the digits after it repeat in the same order. OpenStax writes the repeating block with a bar over it, as in 1.3 for 1.333…, and the calculator uses the same notation.
| Division | Decimal | Repeating block | Block length |
|---|---|---|---|
| 1 ÷ 3 | 0.3 | 3 | 1 |
| 1 ÷ 6 | 0.16 | 6 | 1 |
| 1 ÷ 7 | 0.142857 | 142857 | 6 |
| 1 ÷ 8 | 0.125 | None, terminates | 0 |
| 1 ÷ 11 | 0.09 | 09 | 2 |
| 1 ÷ 12 | 0.083 | 3 | 1 |
| 1 ÷ 13 | 0.076923 | 076923 | 6 |
| 1 ÷ 16 | 0.0625 | None, terminates | 0 |
| 22 ÷ 7 | 3.142857 | 142857 | 6 |
| 43 ÷ 22 | 1.954 | 54 | 2 |
A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5, which is why eighths and sixteenths end while thirds, sevenths and elevenths repeat. Blocks can be long: 1 ÷ 97 repeats every 96 digits. The value 22 ÷ 7 is a common approximation of π, but π itself never repeats.
Divisibility Rules: Know When the Remainder Is 0
These quick tests tell you before dividing whether the remainder will be 0.
| Divisible by | Test | Example |
|---|---|---|
| 2 | Last digit is 0, 2, 4, 6 or 8 | 9,876 ends in 6 |
| 3 | Sum of the digits is divisible by 3 | 9 + 8 + 7 + 6 = 30 |
| 4 | Last two digits form a multiple of 4 | 9,876: 76 = 4 × 19 |
| 5 | Last digit is 0 or 5 | 4,825 ends in 5 |
| 6 | Divisible by both 2 and 3 | 9,876 ÷ 6 = 1,646 |
| 8 | Last three digits form a multiple of 8 | 5,128: 128 = 8 × 16 |
| 9 | Sum of the digits is divisible by 9 | 4,725: 4 + 7 + 2 + 5 = 18 |
| 10 | Last digit is 0 | 1,230 |
| 11 | Alternating sum of the digits is divisible by 11 | 2,728: 8 − 2 + 7 − 2 = 11 |
The tests for 2, 3, 5, 6 and 10 appear in OpenStax Prealgebra. The tests for 4, 8, 9 and 11 follow from place value, and every rule in the table was checked in code against actual division for all numbers from 1 to 100,000.
Long Division with Negative Numbers
Divide the absolute values, then fix the sign: the quotient is negative when exactly one of the numbers is negative. OpenStax uses this approach, for example −7 ÷ 2 = −3.5.
Remainders with negative numbers follow two conventions. Truncated division, which this calculator shows, gives −17 ÷ 5 = −3 R −2, because −3 × 5 + (−2) = −17. Euclidean division keeps the remainder at 0 or above, giving −4 R 3, because −4 × 5 + 3 = −17. Both satisfy the division identity.
Common Long Division Mistakes
- Skipping a zero in the quotient. Every digit you bring down needs a quotient digit above it. In 8,746 ÷ 23 the last step gives 0, and leaving it out turns 380 into 38.
- A remainder as large as the divisor. If 53 − 42 = 11 with a divisor of 7, the quotient digit should have been one larger.
- Misaligned columns. Write each quotient digit directly above the digit you just brought down, and keep products lined up under the digits they came from.
- Moving the decimal point in only one number. When the divisor has decimals, move the point in both numbers by the same number of places.
- Stopping too early with decimals. Add zeros after the decimal point and keep dividing until the remainder is 0, a remainder repeats, or you have one more digit than you need for rounding.
- Dividing by zero. Division by 0 is undefined, so the calculator asks for another divisor.
Related Calculations
To simplify a remainder fraction such as 2/8, the GCF Calculator finds the greatest common factor, and the Fraction Calculator handles mixed numbers. The Prime Factorization Calculator shows whether a denominator has only 2s and 5s, which predicts a terminating decimal.
The Rounding Calculator rounds a long quotient to any place, and the Percent Calculator turns a division into a percentage. For quick arithmetic with powers and roots, use the Scientific Calculator.
Frequently Asked Questions
How do you do long division step by step?
Repeat four steps: divide, multiply, subtract and bring down. For 1,234 ÷ 7, 7 does not go into 1, so start with 12. 7 goes into 12 once; 1 × 7 = 7 and 12 − 7 = 5. Bring down 3 to make 53. 7 goes into 53 seven times; 7 × 7 = 49 and 53 − 49 = 4. Bring down 4 to make 44. 7 goes into 44 six times; 6 × 7 = 42, leaving 2. No digits are left, so 1,234 ÷ 7 = 176 R 2.
How do you write a remainder as a fraction?
Put the remainder over the divisor and write it after the whole number quotient. 1,234 ÷ 7 = 176 R 2, so the answer is 176 2/7. For 1,439 ÷ 4 = 359 R 3, the mixed number is 359 3/4, which equals 359.75 as a decimal. Simplify the fraction if you can: 50 ÷ 8 = 6 R 2 becomes 6 2/8, which simplifies to 6 1/4. To get a decimal instead, keep dividing past the decimal point by adding zeros to the dividend.
How do you do long division with decimals?
First make the divisor a whole number by moving its decimal point to the right, and move the decimal point in the dividend the same number of places. For 47.25 ÷ 3.5, move both points one place: 472.5 ÷ 35. Then divide as usual and put the decimal point in the quotient directly above the decimal point in the dividend. 472.5 ÷ 35 = 13.5. Check by multiplying: 13.5 × 3.5 = 47.25. If the division does not end, add zeros to the dividend and keep going.
What do you do when the divisor does not go into a digit?
Write 0 in the quotient above that digit, then bring down the next digit and try again. For 8,746 ÷ 23, 23 goes into 87 three times with 18 left. Bring down 4 to make 184, and 23 goes into 184 eight times exactly. Bring down 6: 23 does not go into 6, so write 0 in the quotient. The answer is 380 R 6. Leaving out that zero would give 38, an answer ten times too small, so every digit brought down needs a quotient digit above it.
How do you check a long division answer?
Multiply the quotient by the divisor and add the remainder. The result must equal the dividend, and the remainder must be smaller than the divisor. For 1,234 ÷ 7 = 176 R 2, check 176 × 7 + 2 = 1,232 + 2 = 1,234. For 8,746 ÷ 23 = 380 R 6, check 380 × 23 + 6 = 8,746. If the remainder is equal to or larger than the divisor, the quotient digit in that step was too small, and the divisor could have gone in one more time.
Why does long division sometimes give a repeating decimal?
Every remainder is a whole number smaller than the divisor, so there are only a limited number of possible remainders. Once a remainder appears a second time, the same digits follow again forever. For 22 ÷ 7, the remainders are 1, 3, 2, 6, 4 and 5, and then 1 returns, so 22 ÷ 7 = 3.142857 with 142857 repeating. A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5, such as 1/8 = 0.125.
Sources & References
- OpenStax. Prealgebra 2e, 1.5 Divide Whole Numbers (dividend, divisor, quotient, long division steps, remainders, checking by multiplying). openstax.org
- OpenStax. Prealgebra 2e, 5.2 Decimal Operations (dividing a decimal by a whole number, moving the decimal point in both numbers). openstax.org
- OpenStax. Prealgebra 2e, 5.3 Decimals and Fractions (fractions to decimals, repeating decimals and bar notation, negative quotients). openstax.org
- OpenStax. Prealgebra 2e, 2.4 Find Multiples and Factors (divisibility tests for 2, 3, 5, 6 and 10). openstax.org
- MDN Web Docs. Remainder (%) (remainder takes the sign of the dividend; modulo in other languages). developer.mozilla.org
Results are for educational purposes. Every number on this page was recomputed with the same code the calculator uses. Methodology reviewed: 2026.