Long division is the standard pencil-and-paper method for dividing one number by another, building the answer one digit at a time. This calculator shows the entire worked layout — not just the final number — so you can follow exactly how the quotient, remainder, and decimal expansion come together.

The four-step cycle: divide, multiply, subtract, bring down

Long division repeats one short cycle. Divide: see how many times the divisor fits into the current number. Multiply: that digit times the divisor. Subtract: take the product away to find what is left. Bring down: pull the next digit of the dividend alongside the remainder and start again.

For 1,234 ÷ 7, the cycle runs three times: 7 into 12 is 1 (remainder 5), 7 into 53 is 7 (remainder 4), and 7 into 44 is 6 (remainder 2). Reading the digits across the top gives the quotient 176, and the final leftover, 2, is the remainder.

Remainder or decimal?

You can stop at a whole-number remainder — useful when the answer counts indivisible things, like "how many full buses of 7". Or you can continue into a decimal by placing a decimal point in the quotient and bringing down zeros. 1,234 ÷ 7 becomes 176.285714…, where the block 285714 repeats forever.

A decimal terminates only when the divisor's prime factors are just 2s and 5s (so it divides a power of ten). Otherwise the division must eventually reuse a remainder it has seen before, and from that point the digits cycle — a repeating decimal.

Checking your work

The fastest way to catch a slip is the division identity: divisor × quotient + remainder = dividend. For 1,234 ÷ 7 that is 7 × 176 + 2 = 1,234, which matches, so the answer is correct. This calculator runs that check automatically and prints it under the result.

Because the integer arithmetic uses exact big-integer math, the quotient and remainder stay precise even for very large dividends that would lose accuracy in ordinary floating-point calculators.