Long Division Calculator

What this calculator does

When one whole number does not divide neatly into another, you are left with two things: how many whole times it goes in, and a little bit left over. This works both out for you.

Give it the number being divided and the number you are dividing by, and it returns the quotient and the remainder, the two results at the end of a long division. It runs right here in the browser.

Using the calculator

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

It gives you the quotient, the remainder, and the two together in the usual "9 R 2" form. Use whole, positive numbers. Reset clears both boxes.

Quotient and remainder, in plain terms

Say you are sharing 47 sweets among 5 children. Each child gets 9, and there are 2 sweets you cannot share out. The quotient is the 9, how many whole times the divisor fits in. The remainder is the 2, what is left over once you have taken out as many whole lots as you can.

The remainder is always smaller than the divisor. If it were as big as the divisor, you could fit another whole one in, so it would not be left over. When the remainder comes out as 0, the division was exact and the number divided perfectly.

How the long division method reaches it

The tool hands you the end result, but it is worth knowing the method that gets there, because it is how you would do it by hand and it is where those two numbers come from. Long division is a short loop you repeat: divide, multiply, subtract, bring down.

You work through the dividend one digit at a time from the left. At each step you see how many times the divisor fits into what you have so far (divide), multiply to see how much that uses up, subtract to find what is left, then bring down the next digit and go again. The digits you collect along the top build the quotient, and whatever remains at the very end is the remainder.

A worked example with a carry-down

Take 128 ÷ 5.

1. Start with the 12 at the front. 5 goes into 12 twice (2 × 5 = 10), so write 2. Subtract: 12 − 10 = 2 left over.
2. Bring down the next digit, the 8, to sit beside that 2, making 28.
3. 5 goes into 28 five times (5 × 5 = 25), so write 5. Subtract: 28 − 25 = 3.
4. No more digits to bring down, so we stop. The digits along the top read 25, and the 3 is what is left.

So 128 ÷ 5 = 25 remainder 3, which is what the tool returns.

A quick way to check the answer

There is a neat way to be sure a division is right. Multiply the quotient by the divisor, add the remainder, and you should get back the dividend you started with. For our example: 25 × 5 = 125, plus the remainder 3, gives 128. It matches, so the answer is good.

This is not just a trick, it is the actual definition of division for whole numbers: dividend = divisor × quotient + remainder. It always holds, which makes it a reliable check on any long division.

Questions people ask

What is the quotient?

The whole number of times the divisor fits into the dividend. In 47 ÷ 5 = 9 R 2, the quotient is 9.

What is the remainder?

What is left over after taking out as many whole lots as possible. It is always smaller than the divisor. In 47 ÷ 5, the remainder is 2.

What if the number divides evenly?

Then the remainder is 0. For example 20 ÷ 5 = 4 remainder 0, a clean division with nothing left over.

How do I check a long division answer?

Multiply the quotient by the divisor and add the remainder. You should get the original dividend back.

What does "bring down" mean?

After subtracting at each step, you bring the next digit of the dividend down next to the leftover amount, then carry on dividing. It is how the method moves through the number.

References

A note on where this comes from. Splitting a division into a quotient and a remainder is known as Euclidean division: for any whole number dividend and a positive divisor, there is exactly one quotient and one remainder, with the remainder smaller than the divisor, satisfying dividend = divisor × quotient + remainder. The long division method is the standard procedure for finding them by hand. For further reading, see Euclidean division.

1. Euclidean division, guaranteeing a unique quotient and remainder with dividend = divisor × quotient + remainder and a remainder smaller than the divisor.
2. The long division algorithm, the divide, multiply, subtract and bring-down procedure for finding the quotient and remainder.