Long division breaks a division problem into a repeated cycle of four steps — divide, multiply, subtract, bring down — worked one digit at a time from left to right. This calculator shows the full working, not just the final quotient, specifically for anyone re-learning the manual method or checking their own work against it.
Take 936 ÷ 4 as a worked example. Divide: how many times does 4 go into 9 (the first digit)? Twice, with some left over (4 × 2 = 8). Multiply: 4 × 2 = 8. Subtract: 9 − 8 = 1. Bring down: bring down the next digit (3) to make 13. Repeat: how many times does 4 go into 13? Three times (4 × 3 = 12). Subtract: 13 − 12 = 1. Bring down the next digit (6) to make 16. How many times does 4 go into 16? Exactly four times (4 × 4 = 16), subtract to get 0, nothing left to bring down. Reading the quotient digits found at each step (2, 3, 4): 936 ÷ 4 = 234, with no remainder.
A second worked example, this time with a remainder: 179 ÷ 5. 5 goes into 17 three times (5×3=15), subtract to get 2, bring down 9 to make 29. 5 goes into 29 five times (5×5=25), subtract to get 4, nothing left to bring down. Quotient so far: 35, remainder 4. Written as a mixed result: 179 ÷ 5 = 35 remainder 4, or as a decimal, continuing the process by bringing down a zero after the decimal point: 4 becomes 40, 5 goes into 40 exactly 8 times, giving 35.8 with no further remainder.
The "bring down a zero and continue" step is exactly how a remainder becomes a decimal continuation instead of stopping at "remainder 4" — you're not doing anything fundamentally different, just continuing the same divide-multiply-subtract-bring-down cycle into the decimal places, and it can continue indefinitely if the division doesn't terminate cleanly (dividing by 3, for instance, often produces a repeating decimal).
A third worked example with a two-digit divisor: 483 ÷ 21. 21 doesn't go into 4 or 48 alone at the single-digit level the same way, so you work with the first two digits: 21 goes into 48 twice (21×2=42), subtract to get 6, bring down 3 to make 63. 21 goes into 63 exactly three times (21×3=63), subtract to get 0. Quotient: 23, no remainder. Two-digit (and larger) divisors follow the identical four-step cycle; the only added difficulty is that estimating "how many times does the divisor go in" takes a little more trial and error than with single-digit divisors, since you can't just recall a single-digit multiplication fact.
A common mistake is losing track of place value when writing the quotient digits — writing the digits found at each step but misaligning them, which shifts the decimal point in the final answer by a factor of 10. Another common mistake is an error in the "how many times does it go in" estimation step, which then cascades: if you guess too high or too low at any stage, the subtraction step will produce a negative number or a remainder too large to be valid (equal to or greater than the divisor), both clear signals to go back and re-estimate that step.
Long division is also the mechanical process underneath the "decimal doesn't terminate" fact discussed on the Fraction to Decimal Converter — dividing 1 by 3 by hand, you'll notice the remainder at each step (1, then 10, then 1 again) starts repeating, which is exactly why 1/3 = 0.333... repeats forever rather than settling to zero: the division process itself has entered a loop, mechanically guaranteed to repeat once a remainder reappears that's already occurred earlier in the same division.
For the full method taught with additional worked examples, including dividing by two-digit divisors, see How to Do Long Division, Step by Step.