Long Division Calculator
Enter a dividend and divisor to see the quotient, remainder, decimal, and the complete long-division work.
Example: 156 ÷ 7. Dividend: 156. Divisor: 7. Whole numbers, decimals, and negative numbers are all accepted.
Divide whole numbers or decimals with complete long-division steps. See the quotient, remainder, exact fraction, decimal answer, repeating decimals, and every divide, multiply, subtract, and bring-down step.
Enter a dividend and divisor to see the quotient, remainder, decimal, and the complete long-division work.
Example: 156 ÷ 7. Dividend: 156. Divisor: 7. Whole numbers, decimals, and negative numbers are all accepted.
Long division is a step-by-step method for dividing numbers when the division is too large or inconvenient to do mentally. The method breaks one large division problem into smaller divisions that are easier to manage. For example: 156 ÷ 7. Instead of trying to calculate the whole answer at once, long division works through the dividend from left to right. At each stage you divide, multiply, subtract, and bring down. Then you repeat the same cycle until every digit has been used. For 156 ÷ 7, the whole-number result is 22 remainder 2. The exact value can also be written 22 2/7, or 156/7. Its decimal form is 22.285714..., and the digits 285714 repeat. That means the same division problem can have several useful answer forms depending on what you need: a whole-number quotient and remainder, a fraction, a mixed number, or a decimal, and this long division calculator shows all of them together with the full division calculator with steps work.
A division problem has several important terms. Consider 156 ÷ 7 = 22 R2. The dividend is the number being divided; here it is 156. The divisor is the number doing the dividing; here it is 7. The quotient is the result telling how many whole times the divisor fits; here it is 22. The remainder is the amount left over after making as many complete groups as possible; here it is 2. These terms also appear in the traditional long-division setup: the divisor is written outside the division bracket, the dividend is written inside, and the quotient is written above.
Use 156 ÷ 7. Start with the leftmost digit. Can 7 go into 1? No. So consider the first two digits: 15. Ask how many whole times does 7 fit into 15 without going over. The answer is 2. Write 2 in the quotient. Now multiply: 2×7=14. Write 14 under 15. Subtract: 15-14=1. Now bring down the next digit from the dividend: 6. The new working number is 16. Ask how many whole times does 7 fit into 16? Again, 2. Write the second 2 in the quotient. Multiply: 2×7=14. Subtract: 16-14=2. There are no more whole-number digits to bring down. Therefore 156 ÷ 7 = 22 remainder 2. This is the basic long-division cycle: Divide, then Multiply, then Subtract, then Bring Down. That is exactly what this long division calculator with steps displays for any pair of numbers you enter.
Long division works because our number system is based on place value. The number 156 means 1 hundred, 5 tens, and 6 ones. When 7 does not fit into the first digit, 1, the algorithm considers 15 tens. After dividing as many groups of 7 as possible, the leftover amount is combined with the next place-value digit; that is what the bring-down step accomplishes. The algorithm is not randomly moving digits around. It is keeping track of the value that remains after each partial division. That is also why long division works for numbers much larger than 156: the same place-value process can continue through hundreds, thousands, millions, or many more digits.
The quotient is the result of a division. For 20 ÷ 5, the quotient is 4. The division is exact because 5×4=20. For 23 ÷ 5, the whole-number quotient is still 4, but 3 remains. Therefore 23 ÷ 5 = 4 R3. The quotient tells us how many complete groups of the divisor fit inside the dividend.
A remainder is the amount left after the divisor has been subtracted in complete groups as many times as possible. Consider 23 ÷ 5. Five fits into 23 four times. 4×5=20. Subtract: 23-20=3. Therefore the remainder is 3. A valid positive-integer remainder must be smaller than the divisor; if the remainder were 5 or more, another full group could still be divided.
Use Dividend = Divisor × Quotient + Remainder. For 23 ÷ 5 = 4 R3, check: 5×4+3. 20+3=23. That matches the original dividend, so the result is verified. For 156 ÷ 7 = 22 R2, check: 7×22+2 = 154+2 = 156. This verification is one of the easiest ways to catch a long-division mistake, and this calculator performs it automatically every time so you always know how to check long division against the original dividend.
The remainder becomes the numerator. The divisor becomes the denominator. Example: 23 ÷ 5 = 4 R3. Write 4 3/5. The fraction 3/5 represents the portion of one more divisor group that remained. You can also write the entire division as 23/5. The Fraction Calculator can help with simplifying, comparing, adding, or converting fractions once you have written your remainder as one.
If the division leaves a remainder, the calculation can continue past the ones place. Example: 23 ÷ 5. Whole-number result: 4 R3. Instead of stopping, write a decimal point after 4. Append a zero to the remainder: 3 becomes 30 tenths. Now divide: 30 ÷ 5 = 6. Therefore 23 ÷ 5 = 4.6. The remainder disappeared, so the decimal terminates.
Suppose 3 ÷ 8. Eight cannot fit into 3 even once as a whole number. Therefore the whole-number quotient begins with 0. Write 0. Add a decimal point and append a zero: 3.0. Now consider 30. Eight fits into 30 three times. 3×8=24. Remainder: 6. Bring down another zero: 60. Eight fits into 60 seven times. 7×8=56. Remainder: 4. Bring down another zero: 40. Eight fits exactly 5 times. Result: 0.375. Therefore 3/8 = 0.375.
Decimal long division follows the same basic process as whole-number long division, but decimal placement matters. Consider 25.2 ÷ 4. Because the divisor 4 is already a whole number, divide normally. Place the decimal point in the quotient directly above the decimal point in 25.2. The result is 6.3. Check: 6.3×4=25.2.
If the divisor contains a decimal, first make the divisor a whole number. Example: 12.6 ÷ 0.3. Move the decimal in 0.3 one place to the right. That gives 3. You must move the dividend's decimal the same number of places: 12.6 becomes 126. Now calculate 126 ÷ 3 = 42. Therefore 12.6 ÷ 0.3 = 42. Why is that allowed? Because multiplying both numbers by 10 does not change their quotient. 12.6/0.3 and 126/3 represent the same division relationship, so this decimal division calculator logic always keeps the answer exact.
A terminating decimal eventually ends. Examples: 1/2=0.5. 3/4=0.75. 3/8=0.375. 7/20=0.35. When a fraction has been simplified completely, its decimal terminates if the denominator's prime factors contain only 2 and/or 5. For example, 8=2³, so 3/8 terminates. And 20=2²×5, so 7/20 also terminates. This is why some long-division problems stop naturally after a few decimal places.
A repeating decimal contains a pattern of digits that continues forever. Example: 1 ÷ 3 = 0.333333.... The repeating digit is 3. This can be written 0.(3), or with a bar over the repeating digit. Another example: 1 ÷ 7 = 0.142857142857.... The repeating block is 142857. For 156 ÷ 7, the result is 22.285714285714.... The repeating block is 285714. A good repeating decimal calculator division tool should identify the repeating cycle instead of pretending a rounded decimal is exact, which is exactly what the Detect Repeating Decimal option above does.
During long division, the next decimal digit depends on the current remainder. For a fixed divisor, only a limited number of different nonzero remainders are possible. If the remainder ever becomes 0, the decimal terminates. If a previous remainder appears again, the same division steps begin repeating, which creates a repeating decimal cycle. This gives a calculator a reliable mathematical way to detect repetition: track the remainders. When a remainder repeats, the quotient digits generated between the two appearances form the repeating block. This calculator's terminating decimal calculator and repeating-decimal logic both work the same way, by tracking every remainder rather than guessing from a rounded number.
Long division writes out the intermediate multiplication, subtraction, and remainder steps. Short division is a more compressed method often used when the divisor is simple and the intermediate work can be handled mentally. For example, dividing 864 ÷ 4 may be quick enough for short division. But long division is often easier to learn from because every stage is visible. This calculator focuses on long division with the full work shown, which is why it works well as both a long division calculator with work and a plain division calculator with steps.
A fraction is another way of writing division. For example, 3/4 means 3 ÷ 4. Using long division, 3 ÷ 4 = 0.75. Therefore 3/4 = 0.75 = 75%. This relationship connects fractions, division, decimals, and percentages. Use the Percentage Calculator when the main question is converting or comparing percentages, since many percentage calculations ultimately involve this same underlying division.
A ratio such as 3:4 compares 3 with 4. Its numerical first-to-second comparison is 3÷4=0.75. The Ratio Calculator can help simplify, compare, scale, or divide quantities according to ratios once you understand how the underlying division works.
Estimation is a useful way to catch mistakes. Suppose 156 ÷ 7. Nearby easy numbers include 140 ÷ 7 = 20, and 175 ÷ 7 = 25. So the exact result should be somewhere between 20 and 25. The calculator gives 22 remainder 2, which makes sense. If you accidentally calculated 220, estimation would immediately reveal that something went wrong.
When a division does not end exactly, zeros can be appended after a decimal point. Example: 1 ÷ 8. Write 1.000. That does not change the value of 1; it simply gives additional decimal places to continue the division. The process produces 0.125. Appending zeros allows long division to continue into tenths, hundredths, thousandths, and beyond.
Zeros inside a quotient are important placeholders. Example: 1005 ÷ 5. The result is 201. The 0 cannot simply be skipped; it represents the fact that the divisor does not fit into the relevant intermediate place-value portion. A correct long-division algorithm must preserve those zero quotient digits, which is exactly what this calculator's dynamically generated long-division work does for every input.
Yes, but the sign rules are handled separately from the digit-by-digit magnitude calculation. Examples: 12 ÷ 3 = 4. -12 ÷ 3 = -4. 12 ÷ -3 = -4. -12 ÷ -3 = 4. A positive divided by a positive is positive. A negative divided by a positive, or positive divided by a negative, is negative. Two negatives divide to produce a positive. The long-division digits can be worked using the absolute values, then the correct sign is applied to the quotient.
No. Division by 0 is undefined. Consider 10 ÷ 0. If a quotient existed, it would need to be some number q such that 0×q=10. But 0 multiplied by any real number is 0, never 10. Therefore 10÷0 has no ordinary numerical answer. A calculator should never display Infinity as though it were an ordinary quotient, and this one always reports division by zero as undefined instead.
Zero divided by any nonzero number is 0. Example: 0 ÷ 5 = 0, because 5×0=0.
The expression 0÷0 does not have one defined arithmetic value. Many different values multiplied by 0 still produce 0. Therefore there is no unique quotient. The calculator reports this operation as undefined or indeterminate in this context, rather than returning 0 or 1.
This calculator performs numerical long division. It divides numbers such as 156÷7 or 25.2÷4. Polynomial long division is an algebra method used to divide expressions containing variables and powers, such as x³+2x²-x+4 by another polynomial. The procedures share a structural idea, but they operate on different types of mathematical objects. Do not use this calculator as a polynomial-division solver; see the Questions section below for more on this distinction.
Supplied share.google reference could not be resolved to a verified final URL. WebFetch access to that link returned a proxy rejection instructing not to retry, and searching the web for the literal URL did not surface a matching page, so no destination or citation is invented here. The CalculateThisWay explanation above remains the primary walkthrough of how long division works, and the verified reference in Sources & Further Learning below is offered as an optional additional, independent demonstration of the same digit-by-digit method.
Long division is a foundational arithmetic skill. It appears in school arithmetic, where students use it to divide numbers that are not easily handled mentally. It appears in fractions, since fractions can be converted to decimals using division. It appears in percentages, since many percentage calculations ultimately involve division. It appears in ratios and rates, since unit rates such as miles per hour often require division. It appears in money, since costs can be divided across people, payments, or quantities. It appears in measurement, since lengths, weights, areas, and other quantities may be divided into equal parts. It supports algebra preparation, since the structure of long division helps students understand later procedures involving algebraic expressions. And it supports estimation and number sense, since knowing the process helps you determine whether a calculator result is reasonable.
Mixing up the dividend and divisor. In 156 ÷ 7, 156 is the dividend and 7 is the divisor.
Forgetting a quotient digit. Every place-value position matters; sometimes the quotient requires a 0 placeholder.
Multiplying incorrectly. After choosing a quotient digit, multiply it by the divisor accurately.
Subtracting incorrectly. A subtraction error changes every later step.
Forgetting to bring down the next digit. After subtracting, bring down the next unused dividend digit.
Stopping when a decimal is needed. A remainder can be continued by adding a decimal point and zeros.
Moving only one decimal. When the divisor has a decimal, move both the divisor and dividend decimal points by the same number of places.
Putting the decimal in the wrong place. If the divisor is a whole number, the quotient decimal belongs directly above the dividend decimal.
Thinking a rounded decimal is exact. A repeating decimal does not become exact simply because the calculator stops displaying digits.
Failing to check the answer. Use Divisor × Quotient + Remainder = Dividend for whole-number remainder results.
Use this sequence. Step 1, Set Up the Problem: dividend inside, divisor outside. Step 2, Divide: determine how many times the divisor fits into the current working number without going over. Step 3, Multiply: multiply that quotient digit by the divisor. Step 4, Subtract: subtract the product from the working number. Step 5, Bring Down: bring down the next unused digit. Step 6, Repeat: continue Divide, Multiply, Subtract, Bring Down. Step 7, Handle the Remainder: either stop with a remainder, convert the remainder to a fraction, or continue into decimals. Step 8, Verify: check the result mathematically.
Do not leave knowing only that 156÷7 is 22 remainder 2. Leave knowing what long division is, and understanding the dividend and the divisor. Know what the quotient represents and what the remainder represents. Remember the DMSB process: Divide, Multiply, Subtract, Bring Down. Understand why the process works through place value, and know how to check your answer. Know how to write a remainder as a fraction and how to continue a remainder into decimals. Know how to divide when the dividend is smaller than the divisor, and understand decimal placement, including what to do when the divisor contains a decimal. Understand the difference between terminating and repeating decimals, and know why repeating decimals repeat. Understand how division connects to fractions, percentages, ratios, and rates. Know that division by zero is undefined, and understand the difference between numerical long division and polynomial long division. And most importantly: you can see every step that produced the answer. That is what the CalculateThisWay Long Division Calculator should help you understand.
| Concept | Rule / Formula |
|---|---|
| Division Check | Dividend = Divisor × Quotient + Remainder |
| Remainder Rule | 0 ≤ Remainder < |Divisor| |
| Remainder as Fraction | Remainder / Divisor |
| Mixed Number | Quotient + Remainder/Divisor |
| Exact Fraction | Dividend / Divisor |
| Move Decimal Divisor | Multiply dividend and divisor by the same power of 10 |
| Positive ÷ Positive | Positive |
| Negative ÷ Positive | Negative |
| Positive ÷ Negative | Negative |
| Negative ÷ Negative | Positive |
| 0 ÷ Nonzero | 0 |
| Division by 0 | Undefined |
| Terminating Decimal | Reduced denominator contains only factors 2 and/or 5 |
| Repeating Decimal | Reduced denominator has another prime factor |
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Open Calculator ›What is long division?
Long division is a step-by-step method for dividing numbers by working through the dividend from left to right, dividing, multiplying, subtracting, and bringing down digits until every place has been used.
How does long division work?
It repeats a four-step cycle, Divide, Multiply, Subtract, Bring Down (DMSB), for each digit of the dividend until the division is complete.
How do you do long division?
Divide the divisor into the leading digits of the dividend, multiply the quotient digit by the divisor, subtract to find what is left over, bring down the next digit, and repeat.
What are the steps for long division?
Set up the problem, divide, multiply, subtract, bring down, repeat, then handle any remainder and verify the answer.
What does DMSB mean?
DMSB stands for Divide, Multiply, Subtract, Bring Down, the four repeating steps of long division.
What is the dividend?
The dividend is the number being divided. In 156 ÷ 7, 156 is the dividend.
What is the divisor?
The divisor is the number you are dividing by. In 156 ÷ 7, 7 is the divisor.
What is the quotient?
The quotient is the result of division, how many whole times the divisor fits into the dividend. In 156 ÷ 7, the quotient is 22.
What is a remainder?
A remainder is the amount left over after the divisor has been subtracted in complete groups as many times as possible. In 156 ÷ 7, the remainder is 2.
How do you check a long division answer?
Multiply the divisor by the quotient, add the remainder, and confirm the result equals the dividend: Dividend = Divisor × Quotient + Remainder.
How do you write a remainder as a fraction?
Put the remainder over the divisor. For 23 ÷ 5 = 4 R3, the fraction is 3/5, giving the mixed number 4 3/5.
How do you turn a remainder into a decimal?
Add a decimal point and append a zero to the remainder, then keep dividing. For 23 ÷ 5, 3 becomes 30 tenths, and 30 ÷ 5 = 6, giving 4.6.
How do you do long division when the dividend is smaller than the divisor?
Write 0 as the whole-number quotient, add a decimal point and zeros to the dividend, and continue dividing into tenths, hundredths, and beyond.
How do you do long division with decimals?
Divide normally and place the quotient's decimal point directly above the dividend's decimal point once the divisor is a whole number.
Where does the decimal point go in long division?
When the divisor is a whole number, the decimal point in the quotient goes directly above the decimal point in the dividend.
What do you do when the divisor has a decimal?
Move the divisor's decimal point to the right until it is a whole number, then move the dividend's decimal point the same number of places, and divide.
Why do you move both decimal points?
Multiplying both the dividend and divisor by the same power of 10 does not change their quotient, so it is mathematically safe.
How do I divide 156 by 7?
156 ÷ 7 = 22 remainder 2, or 22 2/7, or 22.285714... with the repeating block 285714.
What is 100 divided by 7?
100 ÷ 7 = 14 remainder 2, or 14 2/7, or 14.(285714) as a repeating decimal.
What is 23 divided by 5?
23 ÷ 5 = 4 remainder 3, or 4 3/5, or 4.6 as a decimal.
What is 3 divided by 8?
3 ÷ 8 = 0 remainder 3, or 3/8, or 0.375 as a terminating decimal.
What is a terminating decimal?
A terminating decimal is a decimal that ends. It happens when the reduced denominator's only prime factors are 2 and/or 5.
What is a repeating decimal?
A repeating decimal contains a block of digits that repeats forever, such as 0.333... or 0.142857142857....
How do you know if a decimal repeats?
Track the remainders during long division. If a remainder repeats, the digits produced since it last appeared form a repeating block.
Why does 1 divided by 3 repeat?
Because 3 is not a factor of any power of 10, the remainder in the division of 1 by 3 never becomes 0, so the digit 3 repeats forever.
Why does 1 divided by 8 terminate?
Because 8 = 2³, a power of 2, the division reaches a remainder of 0 after three decimal places, giving 0.125.
How do you write repeating decimals?
Place parentheses or a bar over the repeating digits, such as 0.(3) or 0.3 with a bar, meaning 0.333....
What is short division?
Short division is a compressed version of long division, often done mentally, usually used with a simple one-digit divisor.
What is the difference between long division and short division?
Long division writes out every multiplication, subtraction, and remainder; short division skips the written-out steps and is faster for simple divisors.
Can long division work with negative numbers?
Yes. The digit-by-digit work uses absolute values, and the correct sign, positive or negative, is applied to the final quotient afterward.
Can you divide zero by a number?
Yes. Zero divided by any nonzero number is 0, because that number times 0 equals 0.
Can you divide by zero?
No. Division by zero is undefined because no number multiplied by 0 can produce a nonzero dividend.
What is 0 divided by 0?
0 divided by 0 is undefined or indeterminate, since any number multiplied by 0 equals 0, so there is no single correct quotient.
How can I estimate a division answer?
Round the dividend and divisor to nearby easy numbers and divide those, then check that your exact answer is close to that estimate.
Why do you bring down a zero in long division?
Appending a zero after the decimal point does not change the dividend's value; it simply provides another digit to continue dividing into tenths, hundredths, and beyond.
Why is there sometimes a zero in the quotient?
A zero placeholder shows that the divisor did not fit into that place-value position at all; it must be kept or the answer's value would be wrong.
How are fractions related to division?
A fraction is another way to write division. 3/4 means 3 ÷ 4, which equals 0.75.
How are ratios related to division?
A ratio such as 3:4 compares two numbers, and its numerical value is found by dividing the first number by the second.
Does this calculator do polynomial long division?
No. This calculator performs numerical long division with whole numbers and decimals. Polynomial long division is a separate algebra process involving polynomial expressions.
Whole-number long division processes digits from left to right. Each quotient digit follows Divide, Multiply, Subtract, Bring Down. Remainders are verified using dividend = divisor × quotient + remainder. Exact fractional results are preserved where practical, and simplified using exact greatest-common-factor logic. Decimal continuation appends zeros after the decimal point. Decimal divisors are normalized by multiplying both dividend and divisor by the same power of 10 before the digit-by-digit work begins. Repeating decimal cycles are detected mathematically by tracking every remainder produced; when a remainder repeats, the digits generated since its previous appearance are reported as the repeating block, so this calculator never has to guess a repeating pattern from a rounded decimal or run thousands of redundant decimal steps. Large whole-number inputs use exact BigInt integer arithmetic where practical, and input size is limited to keep the page responsive. For negative inputs, the digit-by-digit work is always performed on absolute values and the correct sign is applied to the quotient and decimal results afterward; whole-number remainder notation is intended primarily for nonnegative instructional inputs. Displayed decimal values may be rounded according to the selected precision. Division by zero, and zero divided by zero, are both rejected as undefined or indeterminate rather than returned as Infinity, NaN, or 0.
Last reviewed: September 24, 2026