Long division

Long division is a method of dividing two numbers, using repeated multiplications and subtractions in a tableau. Because it is easy to do, it is usually taught in schools. There are other methods which are faster, or easier to program with a computer, but they are more difficult to understand and perform manually. If we have a large or complicated division problem, we can use long division to break it down into a series of easier calculations. Long division can also be done on polynomials as well.
Overview.
As with most division problems we have three numbers: the dividend, our first number; the divisor, the second number we divide it by; and the quotient, which is the result. Long division is a kind of algorithm, which means it helps us to find the solution to a problem by following a set of clearly-defined steps:
Examples.
Basic case.
Let's assume we want to divide 780 by 4. To do so with long division, we need to split 780 into digits -- 7 and 8 and 0 -- and then divide each one by 4, carrying any remainders to the next step.
7 / 4 = 1 R 3 -- since we have a remainder of 3, we have to carry this down.
38 / 4 = 9 R 2 -- we carry our remainder of 2 down.
20 / 4 = 5 R 0 -- we have reached the end.
By using long division, we have found that 780 / 4 = 195.
Complex case.
Let's perform a similar calculation where our numbers do not divide easily: 468 / 12
4 / 12 = 0 R 0 -- we cannot perform this division as 4&lt;12, so we have to carry our dividend like a remainder.
46 / 12 = 3 R 10 -- we carry our remainder of 10 down.
108 / 12 = 9 R 0 -- we have reached the end.
By the same process we have found that 468 / 12 = 39.
Decimal Answers.
Let's follow the same process for numbers that give an answer with a decimal because they don't have common factors: 123 / 8
1 / 8 = 0 R 0 -- we cannot perform this division as 1&lt;8, so we have to carry our dividend like a remainder.
12 / 8 = 1 R 4 -- we carry our remainder of 4 down.
43 / 8 = 5 R 3 -- we have reached the end with a remainder, which we have to add to our final answer.
123 / 8 = 15 R 3, which equals 15.375 (15 3/8).