How do you do long division step by step?

Work through the dividend one digit at a time. At each step: divide (how many times does the divisor go into the number so far), multiply (divisor times that digit), subtract (find the new remainder), and bring down (attach the next digit of the dividend to the remainder). Repeat until you run out of digits.

What is the difference between the remainder and the decimal answer?

The remainder is what is left over after you stop at whole numbers, written as "r" plus a number, like 12 r 10. The decimal answer keeps going past the decimal point by bringing down zeros instead of stopping, turning that same remainder into digits like .8333.

Why do some decimals repeat forever?

A remainder can only take on as many values as the divisor allows (from 0 up to one less than the divisor). If you never hit a remainder of 0, you are guaranteed to see a remainder you have already seen before, and from that point the digits repeat in a loop. 1/7 = 0.142857 repeating, over and over, every 6 digits.

How do you turn a remainder into a mixed number?

Put the remainder over the divisor as a fraction, then reduce it. For 10 divided by 3, the quotient is 3 and the remainder is 1, so the mixed number is 3 and 1/3. For 154 divided by 12, the quotient is 12 and the remainder 10 over 12 reduces to 5/6, giving 12 and 5/6.

What do dividend, divisor, quotient, and remainder mean?

The dividend is the number being split up. The divisor is the number you are splitting it into groups of. The quotient is how many whole groups you get. The remainder is whatever is left over that does not fill another whole group.

Can you divide by zero?

No. There is no number that, multiplied by zero, gives you back a nonzero dividend, so division by zero is undefined rather than answered by zero or infinity. Enter any divisor of 1 or more.

Is there a quick way to check if a number divides evenly?

Yes, divisibility rules skip the full calculation for common divisors: a number is divisible by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, by 3 if its digits sum to a multiple of 3, and by 9 if its digits sum to a multiple of 9. Check the divisibility section below for the full list.

Long Division Calculator: Every Step Shown

Enter a dividend and a divisor and this calculator walks the classic long division algorithm with your numbers, one digit at a time, the same way a teacher would on a whiteboard.

How this long division calculator works

Long division is the first real algorithm most of us ever learn, and it is usually taught with one example on a worksheet that never quite looks like the number you are actually stuck on. This page does it with your numbers instead. Type in a dividend and a divisor, pick how you want the answer written, and you get the exact same four moves a teacher would walk you through on a whiteboard: divide, multiply, subtract, bring down, one digit at a time, until there is nothing left to bring down.

Below the answer you get the full narrated steps and a compact version of the traditional bracket layout, with the quotient sitting on top and each subtraction lined up underneath, built from the same working the steps use.

The four moves, taught properly

At every step you are looking at a small number (the digits you have brought down so far) and asking one question: how many whole times does the divisor go into it? That count, from 0 to 9, is the next digit of your quotient. Then you multiply the divisor by that digit, subtract the result from the small number to find what is left over, and bring down the next digit of the dividend to join the leftover. That combined number becomes the next small number, and you ask the same question again.

divide → multiply → subtract → bring down → repeat

The whole algorithm is really just that loop, run once per digit of the dividend. Once you run out of digits to bring down, whatever is left over is your remainder. If it is 0, the division is exact. If it is not, you can stop there, or keep going past the decimal point by bringing down zeros instead of digits, which is exactly what the decimal option above does.

Vocabulary

Term	Meaning
Dividend	The number being split up (in 1548 ÷ 12, that is 1548).
Divisor	The number you are splitting it into groups of (12).
Quotient	How many whole groups you get (129).
Remainder	What is left over that does not fill another whole group (0, here).

Worked example

Divide 1,548 by 12.

Start with the first digit, 1. 12 does not go into 1, so the first quotient digit is 0. Bring down the 5 to make 15: 12 goes into 15 one time (12 x 1 = 12), remainder 3. Bring down the 4 to make 34: 12 goes into 34 two times (12 x 2 = 24), remainder 10. Bring down the 8 to make 108: 12 goes into 108 nine times (12 x 9 = 108), remainder 0.

Reading the quotient digits gives 129, with a remainder of 0. So 1,548 ÷ 12 = 129 exactly.

Remainder, decimal, or mixed number: which one do you want?

These three formats are not different answers, they are the same answer written three ways. Quotient with remainder (129 r 0, or something like 12 r 10) is the version taught first in school and the fastest to compute by hand. It is also the most honest about what actually happened: nothing was rounded or estimated, and the remainder tells you precisely what did not fit evenly.

The decimal format keeps dividing past the remainder by bringing down zeros instead of stopping, which is the same process applied to numbers that are not actually there in the original dividend. Some decimals terminate cleanly (7 ÷ 8 = 0.875 exactly); others repeat forever, because a remainder can only take on so many different values before one repeats, and once a remainder repeats, the digits from that point repeat too. This calculator checks for that and tells you when it happens instead of silently cutting the number off at 6 places as if nothing were going on.

The mixed number format is the remainder written as a fraction of the divisor, then reduced: 10 ÷ 3 becomes 3 and 1/3, not 3.333. It is the right choice whenever the number represents countable things you cannot split into decimals in real life, like leftover eggs from a carton.

A quick divisibility check before you divide

Sometimes you do not need the full division at all, just a yes or no on whether it comes out even. A few rules cover most everyday cases: a number is divisible by 2 if its last digit is even, by 5 if it ends in 0 or 5, and by 10 if it ends in 0. For 3 and 9, add up all the digits: if that sum is divisible by 3, so is the original number; if the sum is divisible by 9, so is the original number. For 4, check whether just the last two digits form a number divisible by 4. None of these save you from doing the division when you actually need the quotient, but they are a fast sanity check on whether the remainder should be 0 before you start.

Working with the pieces long division leaves behind? Reduce a leftover remainder into lowest terms on the fraction calculator, find what a dividend and divisor have in common on the GCF calculator, do exact arithmetic on the decimals it produces with the decimal calculator, or simplify a radical with the square root calculator.

Long Division Calculator