Long Division Calculator

Q: Why does the calculator show both a remainder and a decimal answer?

Long division naturally stops with a whole-number quotient and remainder (for example, 17 divided by 5 is 3 remainder 2). Continuing the same division past the ones place by appending zeros to the remainder produces the decimal form instead (3.4 in that example). This calculator shows both so you can use whichever form fits your problem, such as remainder form for word problems about leftover items, or decimal form for measurements.

Q: How does the calculator handle negative numbers?

The calculator divides the absolute values of the dividend and divisor using the standard long division steps, then reapplies the correct sign to the quotient (negative if exactly one of the two numbers is negative) and to the remainder (matching the sign of the dividend), consistent with how signed integer division is conventionally taught.

Quotient

Remainder

As a Decimal

Step	Bring Down	Divide	Multiply	Subtract

How Long Division Works

Long division breaks a division problem into a repeated sequence of four steps applied digit by digit: divide, multiply, subtract, and bring down. Starting from the leftmost digits of the dividend, you find how many times the divisor fits into the current portion of the dividend (divide), write that digit in the quotient, multiply it by the divisor, subtract the result from the current portion, and then bring down the next digit of the dividend to continue. The process repeats until every digit has been brought down, leaving a final remainder that is smaller than the divisor. This calculator performs that exact algorithm and shows each step in the table above so you can follow along or check your own work.

Quotient, Remainder, and Decimal Form

For any dividend a and divisor b (with b ≠ 0), long division produces a unique quotient q and remainder r satisfying a = bq + r, where 0 ≤ r < |b|. This is the division algorithm from elementary number theory. The remainder can also be expressed as a decimal by continuing the division past the ones place — appending zeros to the remainder and carrying on — which is exactly how the "as a decimal" result above is produced. If you only need the remainder itself, or want to explore how remainders behave with negative numbers or modular arithmetic, try the same values in a general-purpose scientific calculator.

When Long Division Connects to Other Topics

The same repeated-subtraction idea behind long division is also the basis for the Euclidean algorithm used to find the greatest common factor of two numbers — see the GCF calculator if that's what you're actually after. And if your dividend and divisor come from a fraction you're trying to simplify or convert to a decimal, the fraction calculator handles that directly.

Frequently Asked Questions

Why does the calculator show both a remainder and a decimal answer?

Long division naturally stops with a whole-number quotient and remainder (for example, 17 divided by 5 is 3 remainder 2). Continuing the same division past the ones place by appending zeros to the remainder produces the decimal form instead (3.4 in that example). This calculator shows both so you can use whichever form fits your problem, such as remainder form for word problems about leftover items, or decimal form for measurements.

How does the calculator handle negative numbers?

The calculator divides the absolute values of the dividend and divisor using the standard long division steps, then reapplies the correct sign to the quotient (negative if exactly one of the two numbers is negative) and to the remainder (matching the sign of the dividend), consistent with how signed integer division is conventionally taught.