Quotient And Remainder Calculator

What this calculator does

So, you want to divide one whole number by another and get the answer the way you learned it in school, as a whole-number result plus a remainder. This tool does exactly that. Enter a dividend and a divisor, and it returns the quotient and the remainder together.

Two inputs, and both halves of the division come back, no decimals to interpret.

How to use it

1. Enter the dividend, the number being divided.
2. Enter the divisor, the number you are dividing by.
3. Press Calculate.

The two parts of a division

When one whole number does not divide evenly into another, the honest answer has two pieces rather than one. There is the number of whole times the divisor fits, and there is the amount left over that was too small to make another whole group. Together these are the quotient and the remainder, and this tool reports both. This is the form of division you meet before decimals arrive, and it is often the more useful form in real life, where you care how many complete groups you can make and what is left sitting on the side.

What the quotient is

The quotient is the whole-number result of the division: how many complete times the divisor goes into the dividend. If you are dividing 17 by 5, the quotient is 3, because 5 fits into 17 three whole times, accounting for 15. The tool finds this by dividing and then taking the whole-number part, dropping anything after the decimal point. It is the answer to the question "how many full groups can I make?", ignoring for the moment whatever spills over.

What the remainder is

The remainder is what is left once all the whole groups are taken out. Carrying on the same example, after 5 goes into 17 three times to make 15, the leftover is 17 minus 15, which is 2, so the remainder is 2. The remainder is always smaller than the divisor, because if it were as big as the divisor you could fit one more whole group. A remainder of zero means the division came out exactly. This leftover is the same value the modulo calculator gives on its own; this tool simply reports it alongside the quotient.

A worked example

Divide 17 by 5. Five fits into 17 three whole times, so the quotient is 3. Those three groups use up 15, and 17 minus 15 leaves 2, so the remainder is 2. You would read this as "17 divided by 5 is 3 remainder 2." If instead you divided 20 by 5, the quotient would be 4 and the remainder 0, since 5 divides 20 exactly.

Checking the answer

There is a neat way to check any quotient and remainder. Multiply the quotient by the divisor, then add the remainder, and you should get back the original dividend. For the example above, 3 times 5 is 15, plus the remainder 2, gives 17, which is exactly what we started with. This relationship, dividend equals divisor times quotient plus remainder, is the definition of what division with a remainder means, and it is worth remembering as a quick sanity check. For just the leftover on its own, the modulo calculator is the companion tool.

Questions people ask

What are the quotient and remainder?

The quotient is how many whole times the divisor fits into the dividend; the remainder is what is left over after those whole groups.

Why is the remainder always smaller than the divisor?

Because if the leftover were as large as the divisor, you could fit one more whole group into it.

What does a remainder of zero mean?

That the division is exact: the divisor goes into the dividend a whole number of times with nothing left over.

How can I check the result?

Multiply the quotient by the divisor and add the remainder. It should equal the original dividend.

How is this different from modulo?

Modulo gives only the remainder. This tool gives both the quotient and the remainder together.

References

On division with a remainder. Dividing one whole number by another gives a quotient and a remainder, where the dividend equals the divisor times the quotient plus the remainder.

1. Eric W. Weisstein, "Quotient," from MathWorld, a Wolfram resource, on the quotient as the result, or integer part, of a division.
2. Eric W. Weisstein, "Long Division," from MathWorld, a Wolfram resource, on dividing to obtain a quotient and remainder.