📝 Long Division Calculator (with Steps)
7439 ÷ 12 = 619 r 11 — with every bring-down step laid out the way it's taught, plus the exact decimal (619.91(6), repetend in parentheses).
619 r 11
quotient · remainder
619.91(6)
exact decimal — repetend in ( )
| Step | Bring down | Working value | ÷ 12 → | Subtract | Remainder |
|---|---|---|---|---|---|
| 1 | 7 | 7 | 0 | − 0 | 7 |
| 2 | 4 | 74 | 6 | − 72 | 2 |
| 3 | 3 | 23 | 1 | − 12 | 11 |
| 4 | 9 | 119 | 9 | − 108 | 11 |
Read each row as one long-division step: bring down the next digit, divide the working value by the divisor to get the next quotient digit, subtract, carry the remainder. The quotient digits down the "→" column spell 619.
BigInt arithmetic — 30-digit dividends divide exactly. Repeating decimals are detected and shown with the repetend in parentheses. Runs locally.
How the long division calculator (with steps) works
The calculator performs textbook long division and shows it as a step table: bring down the next digit of the dividend, divide the working value by the divisor to get the next quotient digit, subtract the product, carry the remainder to the next step. After the integer phase you get quotient and remainder — and if you want the decimal, the division simply continues past the point, with cycle detection on the remainders so a repeating expansion is identified exactly and written with the repetend in parentheses (1 ÷ 12 = 0.08(3)). Everything runs on arbitrary-precision integers, so a 30-digit dividend divides as exactly as a 3-digit one.
The steps are the product here: long division is taught as an algorithm, and checking homework means checking the algorithm's intermediate lines, not just the answer. The repetend detection settles the classic confusion between "the calculator ran out of screen" and "the decimal actually repeats" — every rational division either terminates or repeats, and this shows which, with proof.
Frequently asked questions
How does long division work, step by step?
Take digits of the dividend left to right. At each step: bring down the next digit, see how many whole times the divisor fits into the working value (that's the next quotient digit), subtract that multiple, and carry the remainder into the next step. The table shows each of these lines for your numbers.
What do quotient and remainder mean?
Dividend = divisor × quotient + remainder, with the remainder smaller than the divisor. 7439 = 12 × 619 + 11, so 7439 ÷ 12 is 619 remainder 11.
How do I get the decimal answer?
The division continues past the decimal point automatically: append a zero to the remainder and keep dividing. The tool does this with cycle detection, so it shows either the exact terminating decimal or the repeating form with the repetend in parentheses.
Why does the decimal repeat for some divisions?
Because there are only so many possible remainders (fewer than the divisor) — once a remainder recurs, the digits cycle forever. Divisions whose reduced divisor has only factors 2 and 5 terminate; all others repeat.
Is there a size limit?
Dividends up to 30 digits keep the step table readable; the arithmetic itself is exact BigInt at any size. Nothing you enter leaves your browser.