Division Calculator
This division calculator divides one number by another and walks the long division out digit by digit, then keeps going into the decimal places. You get the quotient, the whole-number answer with its remainder, the decimal answer and the fraction form together.
How to use the division calculator
- Type the dividend — the number being divided — into the first box.
- Type the divisor, the number you are dividing by, into the second.
- Read the quotient at the top. The results redraw as you type, so there is nothing to submit.
- Underneath, the working shows each step of the long division, the whole-number answer with its remainder, and the same division written as a simplified fraction.
Leave the divisor at zero and you get an explanation rather than an answer, because division by zero has no result. That is covered further down the page.
Dividend, divisor, quotient, remainder
The four words show up in every set of instructions about division, and mixing them up is the quickest way to type a problem in backwards.
- Dividend — the number being split up. In 476 ÷ 12 it is 476.
- Divisor — how many parts you are splitting it into, or how big each part is. Here it is 12.
- Quotient — the answer. It is 39 as a whole number, or 39.6666… as a decimal.
- Remainder — what is left over when you stop at whole numbers. Here it is 8.
The reverse form is the useful one. 12 × 39 + 8 = 476, so the answer checks out. If that sum does not come back to the dividend, something in the working is wrong. When the remainder itself is the thing you care about, the remainder calculator shows it on its own, negatives included.
Long division, step by step
Long division works one digit of the dividend at a time, left to right. At each step you ask how many times the divisor fits into what you are holding, write that digit in the answer, subtract, and bring the next digit down.
Example: 476 ÷ 12
Take the digits of 476 in order.
That gives 39 remainder 8. To carry on into decimals, put a point after the 39 and start adding zeros to the remainder:
The remainder 8 has come back, so the 6 repeats forever: 476 ÷ 12 = 39.6666…, usually written 39.6 with a bar over the 6. As a fraction it is 119/3.
Example: 945 ÷ 7
This one ends cleanly with no remainder at all.
So 945 ÷ 7 = 135 exactly. Check it the reverse way: 7 × 135 = 945.
A remainder that repeats is your signal to stop. Once you see the same remainder twice, the digits between the two sightings are the repeating block, and writing more of them adds nothing.
Will the decimal stop or repeat?
You can tell before you divide. Write the division as a fraction, cancel it down to its lowest terms, then look at the prime factors of the denominator.
The reason is that our decimal system is built on tens, and 10 = 2 × 5. A denominator made only of 2s and 5s can be scaled up into a power of ten, which is exactly what a finite decimal is. A factor of 3 or 7 can never be scaled into a power of ten, so the division never closes.
| Division | Simplified | Denominator factors | Decimal |
|---|---|---|---|
| 7 ÷ 8 | 7/8 | 2 × 2 × 2 | 0.875, terminates |
| 3 ÷ 20 | 3/20 | 2 × 2 × 5 | 0.15, terminates |
| 6 ÷ 15 | 2/5 | 5 | 0.4, terminates |
| 1 ÷ 6 | 1/6 | 2 × 3 | 0.1666…, recurs |
| 5 ÷ 12 | 5/12 | 2 × 2 × 3 | 0.41666…, recurs |
| 1 ÷ 7 | 1/7 | 7 | 0.142857142857…, recurs |
Note the 6 ÷ 15 row. The 3 in 15 disappears when the fraction cancels to 2/5, and the decimal terminates after all. Always simplify first. The longest a repeating block can be is one less than the divisor, which is why sevenths repeat in blocks of six digits.
Dividing by a decimal
Long division wants a whole-number divisor. If you have a decimal one, multiply both numbers by the same power of ten until the divisor is whole. The quotient does not change, because you have scaled both sides of the division equally.
Look at how many places the divisor’s point has to move, then move the dividend’s point the same number of places, adding zeros if you run out of digits. Only the divisor needs to become whole; the dividend can stay a decimal, as in 4.5 ÷ 0.5 → 45 ÷ 5 = 9.
Why you cannot divide by zero
Division is the reverse of multiplication. Saying 144 ÷ 12 = 12 is the same as saying 12 × 12 = 144. So 5 ÷ 0 is asking: what number, multiplied by 0, gives 5?
Nothing does. Every number multiplied by 0 gives 0, so no answer exists. The division is undefined, and undefined is not a value you can carry forward into the next step.
0 ÷ 0 fails for the opposite reason. Every number multiplied by 0 gives 0, so every number is an answer, and a question with infinitely many equally good answers has no single one.
Common mistakes
- Entering the numbers the wrong way round. 476 ÷ 12 and 12 ÷ 476 are entirely different sums. Division is not commutative.
- Dropping the leading zero. When the divisor does not fit into the first digit, that digit of the quotient is 0 and it still occupies a column. Losing it shrinks the answer by a factor of ten.
- Forgetting to bring a digit down. Every digit of the dividend gets used, in order, including zeros.
- Reporting a remainder without its divisor. “Remainder 8” only means something alongside “divided by 12”. As a fraction that leftover is 8/12, which simplifies to 2/3.
- Mixing the two answer formats. 39 remainder 8 and 39.666… say the same thing. Writing 39.8 mixes them and is wrong.
- Rounding a recurring decimal too early. If the result feeds into more arithmetic, keep the fraction and round at the end.
- Treating a remainder as a leftover you can ignore. When you are dividing objects, the remainder often needs a decision: 100 items in boxes of 12 is 8 full boxes and a ninth box holding 4.
Turning an “improper” answer such as 119/3 into a mixed number is a related job, and the improper fraction calculator does that conversion with the division shown. To check any division in reverse, multiply the quotient back up with the multiplication calculator.
Frequently asked questions
What is 476 divided by 12?
476 ÷ 12 = 39.6666…, or 39 remainder 8 as a whole-number answer. The long division runs 12 into 47 three times with 11 left, then 12 into 116 nine times with 8 left. As a fraction it simplifies to 119/3, and the 6 in the decimal repeats forever.
What is 144 divided by 12?
144 ÷ 12 = 12 exactly, with no remainder. Working it as long division: 12 into 14 goes once with 2 left, then 12 into 24 goes twice with nothing left, giving 12. Check it backwards with 12 × 12 = 144.
Why can’t you divide by zero?
Because division asks a multiplication question in reverse. 5 ÷ 0 means “what times 0 gives 5?”, and nothing does, since anything times zero is zero. So the answer is undefined rather than infinity. 0 ÷ 0 is undefined too, but because every number would work, not none.
What is the difference between a remainder and a decimal answer?
They are two ways of reporting the same leftover. 476 ÷ 12 is 39 remainder 8 if you stop at whole numbers, or 39.6666… if you keep dividing. The remainder 8 becomes the fraction 8/12 = 2/3, and 2/3 as a decimal is 0.6666…. Use remainders for countable things, decimals for measurements.
How do you know if a division will give a repeating decimal?
Write it as a fraction, cancel it to lowest terms, and factor the denominator. If only 2s and 5s remain, the decimal stops. Any other prime factor makes it repeat. 7/8 stops because 8 = 2³; 5/12 repeats because 12 contains a 3.
How do you divide by a decimal?
Multiply both numbers by whatever power of ten makes the divisor a whole number. The answer is unchanged because you scaled both sides equally. 4.5 ÷ 0.15 becomes 450 ÷ 15 = 30, and 7.2 ÷ 0.8 becomes 72 ÷ 8 = 9.
How do you divide by a fraction?
Flip the fraction over and multiply. 6 ÷ 2/3 becomes 6 × 3/2 = 9. This looks strange until you read it as a question: how many two-thirds fit into 6? Three of them fit in each whole unit, so nine fit in six.
What happens when the dividend is smaller than the divisor?
You get an answer below 1, and the whole-number part of the quotient is 0. For 7 ÷ 12 the division starts straight after the decimal point: 12 into 70 goes 5 times with 10 left, and so on, giving 0.58333…. As a remainder statement it is 0 remainder 7.
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