Long Division Calculator
Divide any two integers with step-by-step long division. Shows quotient, remainder, decimal result, and the full long division process as text.
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How to use this calculator
Long division finds how many times the divisor fits into the dividend (quotient) and what is left over (remainder). The decimal form continues dividing the remainder.
- 1
Enter the dividend (the number being divided) in the first field.
- 2
Enter the divisor (the number you are dividing by) in the second field.
- 3
The quotient, remainder, decimal result, and step-by-step long division are shown.
- 4
Negative inputs are handled — the sign of the quotient follows integer division rules.
Frequently asked questions
How do the signs of the quotient and remainder work?
The quotient is negative when exactly one of the two numbers is negative, and the division truncates toward zero. The remainder takes the sign of the dividend. So −847 ÷ 13 gives −65 remainder −2, while 847 ÷ −13 gives −65 remainder 2, and −847 ÷ −13 gives 65 remainder −2. The verification row confirms each case by recomputing divisor × quotient + remainder.
Why do I get an error when I type a decimal?
The tool performs integer long division, so both fields must be whole numbers; 7.5 ÷ 2 is rejected rather than rounded. To divide decimals, shift the decimal point in both numbers by the same power of ten until they are integers: 7.5 ÷ 2 becomes 75 ÷ 20, which gives 3 remainder 15 and a decimal result of 3.75.
Where is the “Decimal result” cut off?
It is rounded to eight decimal places and trailing zeros are dropped. 1 ÷ 7 shows 0.14285714, and the real decimal repeats forever with a cycle of six digits (142857), which this output does not mark. For 1000 ÷ 8 the decimal is exactly 125.
Why are only some steps shown?
The step list covers the first eight digits of the dividend. For 1,234,567,890 ÷ 7 you see eight steps and the last two digits are not walked through, though the quotient and remainder at the top still account for all ten. Short dividends, such as three-digit numbers, show every step.
What does a step with quotient 0 mean?
It means the divisor does not yet fit into the digits brought down so far, and the next digit is brought down in the following step. In 847 ÷ 13, the first step is 8 ÷ 13 = 0 with a remainder of 8; the 4 is then brought down to make 84.
What happens with a divisor or dividend of zero?
A divisor of 0 returns “Divisor cannot be zero”. A dividend of 0 returns a quotient, remainder and decimal of 0 without step-by-step working. There is no special output for zero remainders other than the line “Exact division? Yes”.
How large can the numbers be?
Up to 9,007,199,254,740,991 (2⁵³ − 1) in absolute value, which is the largest integer the underlying number type represents exactly. Larger values are refused instead of producing a plausible but wrong answer. The decimal line of a very large dividend may still be limited by 15 to 16 significant digits.
Long division with quotient, remainder and steps
How the steps are built
Long division works left to right through the dividend’s digits. At each step you bring down the next digit, see how many times the divisor fits, subtract, and carry the remainder forward. The calculator prints each of those moves as a line such as 84 ÷ 13 = 6 (13 × 6 = 78, remainder 6), then reports the final quotient, the remainder, the decimal value, and a check that divisor × quotient + remainder returns the dividend.
| Division | Quotient | Remainder | Decimal |
|---|---|---|---|
| 847 ÷ 13 | 65 | 2 | 65.15384615 |
| 1000 ÷ 8 | 125 | 0 | 125 |
| 5 ÷ 13 | 0 | 5 | 0.38461538 |
| 1234567890 ÷ 7 | 176366841 | 3 | 176366841.42857143 |
| −847 ÷ 13 | −65 | −2 | −65.15384615 |
Worked example: 847 ÷ 13
The first digit, 8, is smaller than 13, so step 1 gives 0 with remainder 8. Bring down the 4 to make 84: 13 fits 6 times (78), leaving 6. Bring down the 7 to make 67: 13 fits 5 times (65), leaving 2. Reading the quotient digits gives 65 remainder 2, and the check line confirms 13 × 65 + 2 = 847. The decimal continues the same process past the last digit, ending at 65.15384615.
Worked example: a negative dividend
For −847 ÷ 13 the digit steps are the same as for 847, because the work is done on absolute values and the signs are applied afterwards. The result reads −65 remainder −2 and the verification line shows 13 × −65 + −2 = −847. Some textbooks and programming languages instead insist on a non-negative remainder, which would give −66 remainder 11; this calculator uses truncation toward zero, so compare conventions if your course specifies one.
Remainders and exact division
A remainder of 0 means the divisor divides the dividend exactly, as in 1000 ÷ 8 = 125, and the output says so. When the dividend is smaller than the divisor, as in 5 ÷ 13, the quotient is 0 and the remainder is the dividend itself. A non-zero remainder r always satisfies 0 ≤ r < divisor in absolute terms, which is a good check on your own working.
Limits
Only whole numbers are accepted, up to 2⁵³ − 1 in absolute value. The step list covers the first eight digits of the dividend, and the decimal result is rounded to eight places without flagging repeating digits. Decimal division needs both numbers scaled to integers first.
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