Divide one whole number by another and report an exact integer quotient with its remainder. Beside quotient and remainder, the output shows the operation used to obtain it.
Euclidean division writes a nonnegative dividend as divisor × quotient + remainder, with the remainder smaller than the positive divisor. Those two outputs fully reconstruct the starting number.
The meaning of quotient and remainder follows from the relationship, so a different setup can produce a valid answer to a different question.
Bring down dividend digits from left to right. At each stage choose the largest quotient digit whose product with the divisor does not exceed the current partial dividend. One useful next step from Long Division is remainder arithmetic.
Dividing 98,765,432,109,876,543,210 by 123,456,789 gives quotient 800,000,007,370 and remainder 82,959,280.
Batch sizing, packaging, clock cycles, and modular arithmetic often need both complete groups and leftovers rather than a rounded decimal quotient. A related application of Long Division is division check.
A zero divisor is undefined. This page accepts nonnegative dividends and positive divisors so the quotient-and-remainder convention stays unambiguous.
Review the sign, scale, and unit of quotient and remainder after entering dividend and divisor.
The cleanest input audit is to restate the problem using dividend and divisor. If that sentence sounds wrong, correct the assignment before asking for quotient and remainder.
Increasing the dividend by one normally increases the remainder by one until it wraps to zero and the quotient increases. The pattern also provides a quick estimate of whether a revised result is plausible.
The formula and result serve different readers: the formula shows what was done, and the rounded quotient and remainder communicates scale. Keep both when the work needs review.
Integer division preserves quotient and remainder separately; decimal division combines them into a fractional value. The wording of the problem should decide which operation is appropriate.
A screenshot is unnecessary when the shown formula and the supplied inputs (dividend and divisor) are saved in plain text. Include the rounding rule if the reported quotient and remainder is approximate.
The dividend is not always an exact multiple of the divisor.
Multiply divisor by quotient and add remainder.
No. A valid Euclidean remainder is smaller than the divisor.
No; it reports complete integer groups and the leftover.