Long Division Calculator

Long division is a written method for dividing large numbers by breaking the job into small, repeated steps. You divide the leading digits of the dividend by the divisor and write that digit in the quotient. Then you multiply, subtract and bring down the next digit. The cycle repeats until every digit has been used, and whatever is left is the remainder.

The dividend is the number being divided, and the divisor is the number you divide by. The quotient is the answer, and the remainder is what cannot be shared evenly. In 845 ÷ 7, the dividend is 845, the divisor is 7, the quotient is 120 and the remainder is 5. These names appear in the steps panel, so they are worth learning once.

Type the dividend and the divisor, then press Calculate. Choose Remainder for a whole-number quotient with a remainder, or Decimal to keep dividing past the decimal point. In Decimal mode, Decimal places can stay on Auto or be set from 0 to 20.

The written layout appears under the answer, with the quotient above the bracket and each subtraction lined up below. Turn on Show Steps for a sentence explaining every line in plain words. The Swap button exchanges the two numbers, and a check line multiplies the answer back to prove it.

Each cycle starts by dividing the current partial number by the divisor and writing the whole-number result in the quotient. That digit is multiplied by the divisor, and the product is subtracted from the partial number. The next digit of the dividend is then brought down beside the difference. If the new number is still smaller than the divisor, a zero goes into the quotient.

Decimals follow the same cycle with one extra step at the start. When the divisor has a decimal point, both numbers are multiplied by the same power of ten until the divisor is whole. Past the last digit of the dividend, zeros are brought down to continue into decimal places. If a remainder repeats, the digits between the two matching remainders repeat forever.

These examples move from a clean division to remainders, repeating decimals and decimal divisors. Each one states the input, the answer and what the result means in practice.

Enter any example above to see its full written layout. The check line under each answer multiplies the quotient back so you can trust the result.

Programming languages split long division into two operators: one for the quotient and one for the remainder. JavaScript uses Math.trunc(a / b) and the % operator, while Python offers // and % or the combined divmod function. The results match for positive numbers but differ for negatives, which is a common source of bugs.

JavaScript truncates toward zero, so -7 % 2 is -1, and BigInt division also truncates. Python floors toward negative infinity, so -7 // 2 is -4 with remainder 1. For exact fractions such as 22/7, Python's Fraction type avoids rounding entirely.

const dividend = 845, divisor = 7;
console.log(Math.trunc(dividend / divisor)); // 120
console.log(dividend % divisor);             // 5

// % keeps the sign of the dividend
console.log(-7 % 2);   // -1
console.log(-7n / 2n); // -3n, BigInt division truncates toward zero

print(divmod(845, 7))   # (120, 5)
print(-7 // 2, -7 % 2)  # -4 1, Python floors toward negative infinity
print(1 / 7)            # 0.14285714285714285

from fractions import Fraction
print(Fraction(22, 7))  # 22/7, kept exact instead of rounded

The calculator divides digit by digit with exact integer arithmetic, just as you would on paper. It detects a repeating decimal by watching for a remainder that has appeared before, then marks the repeating block with a bar. Auto mode shows up to 60 decimal digits, and longer cycles are rounded to 20 places and labeled approximate.

Dividends and divisors can have up to 15 digits each, including decimal places. All work happens in your browser, and no numbers are sent to a server or stored. Your inputs disappear as soon as you close or refresh the page. The site's other math calculators follow the same rule.

Most long division errors happen in the bring down step or when a zero is needed in the quotient. Others come from subtracting incorrectly or placing the decimal point in the wrong column. The table lists each mistake with a quick way to catch it.

The simplest check is to multiply the quotient by the divisor and add the remainder. If the total does not equal the dividend, one of the steps went wrong. The tool shows this check under every answer, and it also explains the messages you may see for invalid input.

Long division writes every multiplication and subtraction, which makes it the easiest method to check. Short division keeps the subtractions in your head and suits single-digit divisors. Chunking, also called partial quotients, subtracts easy multiples like 10 or 100 times the divisor and adds them up at the end.

This long division calculator shows the full written method because that is what most homework requires. If you only need the number, the instant-answer tool is faster, and the table below shows when each method fits best. For checking multiplication the other way, try the long multiplication calculator.