Long Division Calculator
Calculate integer long division quotient and remainder.
The algorithm, step by step
Long division breaks an awkward division into a repeating four-step cycle: divide, multiply, subtract, bring down. Work left to right through the dividend, asking at each position how many times the divisor fits, writing that digit in the quotient, subtracting the product, and bringing down the next digit. Repeat until nothing remains to bring down.
Two rules keep it honest. The remainder at every stage must be smaller than the divisor — if it is not, the quotient digit was too small. And when the divisor does not fit at all, write a zero in the quotient rather than skipping the position; omitting that zero silently shifts every later digit and is the single most common source of a wrong answer.
To continue past the whole part, add a decimal point and bring down zeros. Terminating decimals occur when the simplified denominator has only 2s and 5s as prime factors; anything else repeats, and the repeat is guaranteed to start within divisor − 1 digits, because there are only that many possible remainders. Check any result by multiplying quotient by divisor and adding the remainder.
Frequently Asked Questions
What is long division?
Long division breaks down dividing large numbers into steps: Divide, Multiply, Subtract, and Bring down.
How does long division work?
Divide, multiply, subtract, bring down, repeat. At each step you find how many times the divisor fits into the current portion of the dividend, subtract that product, and bring down the next digit. The process terminates when there are no digits left, leaving a remainder, or continues past the decimal point for a decimal answer.
What is the difference between a remainder and a decimal answer?
The remainder is what is left over when you stop at whole numbers: 17 divided by 5 is 3 remainder 2. Continuing past the decimal point converts that remainder into a fraction of the divisor: 3.4. Both are correct - remainders matter in modular arithmetic and in problems where partial units are meaningless.
Why do some divisions repeat forever?
A fraction terminates in decimal only if its denominator, in lowest terms, has no prime factors other than 2 and 5. One third gives 0.333... because 3 is neither. The repeating block can never be longer than one less than the denominator, which is why 1/7 repeats with period 6.