Long Division Calculator
Divide with the full long-division layout: every bring-down, each quotient digit, the remainder, and the decimal with its repeating block marked.
Long Division Calculator: with the default inputs, quotient (whole part) is 176.
Goes under the division bracket. Whole numbers up to a trillion.
Goes outside the bracket. Must be at least 1 — nothing can be divided by zero.
- Remainder
- 2
- Decimal answer
- 176.(285714)A bracketed block repeats forever.
- Repeating block
- 285714
- Length of the repeating block
- 6
- As a decimal number
- 176.2857142857
- Check
- 7 × 176 + 2 = 1,234divisor × quotient + remainder should equal the dividend.
Assumptions
- Whole, non-negative dividend and divisor; signs are handled by the user.
- Every intermediate value stays exact because the dividend is capped at 10¹² and the divisor at 10⁹.
- The decimal expansion is computed to at most 240 places before being reported as truncated.
| Step | Bring down | Working number | Quotient digit | Subtract 7 × digit | Left over |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 0 | − 0 | 1 |
| 2 | 2 | 12 | 1 | − 7 | 5 |
| 3 | 3 | 53 | 7 | − 49 | 4 |
| 4 | 4 | 44 | 6 | − 42 | 2 |
Reading the quotient-digit column top to bottom gives 0176; dropping leading zeros gives 176. The last "left over" is the remainder.
| Decimal place | Working number | Digit | Subtract | Left over | |
|---|---|---|---|---|---|
| 1 | 20 | 2 | − 14 | 6 | ◀ the block starts here |
| 2 | 60 | 8 | − 56 | 4 | |
| 3 | 40 | 5 | − 35 | 5 | |
| 4 | 50 | 7 | − 49 | 1 | |
| 5 | 10 | 1 | − 7 | 3 | |
| 6 | 30 | 4 | − 28 | 2 |
The left-over 2 has appeared before, at decimal place 1. From here every step repeats, so the digits "285714" repeat forever.
How this is worked out
The formula
At each step: working = (previous remainder × 10) + next digit
quotient digit = ⌊ working ÷ divisor ⌋
new remainder = working − (quotient digit × divisor)
dividend = divisor × quotient + remainder, with 0 ≤ remainder < divisor
Past the decimal point the "next digit" is always 0. Because every remainder is one of
the divisor's 0…(divisor − 1) possible values, a remainder must eventually repeat — which
is why every fraction is either terminating or repeating, never random.Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Dividend (the number being divided)
- Goes under the division bracket. Whole numbers up to a trillion.from 0 to 1000000000000 · whole numbers only · defaults to 1234
- Divisor (the number you divide by)
- Goes outside the bracket. Must be at least 1 — nothing can be divided by zero.from 1 to 1000000000 · whole numbers only · defaults to 7
What you get back
- Quotient (whole part)main answer
- Remainder
- Decimal answer
- A bracketed block repeats forever.
- Repeating block
- Length of the repeating block
- As a decimal number
- Check
- divisor × quotient + remainder should equal the dividend.
What this assumes
- Whole, non-negative dividend and divisor; signs are handled by the user.
- Every intermediate value stays exact because the dividend is capped at 10¹² and the divisor at 10⁹.
- The decimal expansion is computed to at most 240 places before being reported as truncated.
About this calculator
Long division is the algorithm you were taught at school and then, quite reasonably, stopped writing out. This calculator writes it out for you: every bring-down, every quotient digit, every subtraction and every left-over, in a table you can copy onto paper. The answer is the least interesting part of the output.
How to read the layout
The dividend is the number being divided, the divisor is what you are dividing by. The first table has one row per digit of the dividend. Each row shows the digit brought down, the "working number" it forms with whatever was left over from the row above, how many times the divisor fits into that working number (the quotient digit), what you subtract, and what is left. Read the quotient-digit column downwards and you have the answer; leading zeros are just placeholders and get dropped.
The second table carries on past the decimal point. There are no more digits to bring down, so you bring down a zero each time — which is exactly what "adding a decimal point and a zero" means.
Remainders, and why decimals repeat
The remainder is what is left when the divisor no longer fits: 1234 ÷ 7 is 176 with 2 left over, because 7 × 176 = 1232. The check line at the bottom of the steps re-multiplies for you.
Once you go past the decimal point, something forced happens. Every remainder is a whole number between 0 and divisor − 1, so there are only finitely many of them. Either one is 0 — the division terminates — or a remainder you have already seen comes round again, and from that moment the digits must repeat in the same cycle forever. That is why 1 ÷ 7 = 0.142857142857…, with a six-digit block, and why no fraction of whole numbers ever produces a non-repeating decimal like π. The repeating block is shown in brackets, and the second table marks the exact row where the cycle closes.
The period can never be longer than divisor − 1, and it hits that maximum for divisors like 7, 17 and 19. A divisor whose only prime factors are 2 and 5 always terminates, because those are the prime factors of ten.
Limits
Both numbers must be whole and positive: work the sign out separately, since a negative divided by a positive is negative and two negatives make a positive. The dividend is capped at a trillion and the divisor at a billion so that every intermediate value stays exactly representable — no rounding creeps into any row. The decimal expansion stops after 240 places; a divisor with a longer period than that gets a truncated decimal and a warning rather than a wrong repeating block.
Frequently asked questions
▸What is the remainder in long division?
Whatever is left over after the divisor has been taken out as many whole times as possible. It is always smaller than the divisor, and divisor × quotient + remainder always rebuilds the dividend.
▸Why does 1 ÷ 7 repeat with six digits?
There are only six possible non-zero remainders when you divide by 7, so once you go past the decimal point one of them has to come round again. It happens after six steps, and the digits then repeat forever.
▸Which fractions give a terminating decimal?
Exactly those whose divisor, in lowest terms, has no prime factors other than 2 and 5 — the prime factors of ten. So halves, quarters, fifths, eighths and twentieths terminate; thirds, sevenths and elevenths repeat.
▸Can I divide by zero?
No. There is no number that multiplied by zero gives a non-zero dividend, so the division has no answer. The calculator refuses rather than returning infinity.
▸How do I do long division with decimals in the numbers?
Multiply both numbers by 10 until they are whole — the quotient is unchanged. 12.5 ÷ 0.4 is the same as 125 ÷ 4. The remainder, though, is scaled by the same factor, so scale it back afterwards.
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