When undertaking long division there are a variety of methods of varying complexity. One of the most simple and common ways involves breaking the number being divided down in to more manageable chunks. In undertaking long division it is important to have a grasp of the mathematical terminology used regarding the numbers involved. The number being divided is the 'dividend' and the number by which it is divided is the 'divisor'. The numbers yielded from the process of division are 'quotients', the number left over from the quotient after a round of division is the 'remainder.'
For example:
11 ÷ 5 = 2 (with 1 left over)
11 is the dividend.
5 is the divisor.
2 is the quotient.
1 is the remainder.
Things You'll Need
 Paper
 Pen or pencil

Take the same number of digits from the front of the dividend as there are in the divisor.
For example:
a) If you are calculating 849 ÷ 37, take the 84.
b) If you are calculating 5642 ÷ 126, take the 564.

Create a multiplication table for the divisor.
For example:
a)
1 x 37 = 37
2 x 37 = 74
3 x 37 = 111
4 x 37 = 148
5 x 37 = 185
b)
1 x 126 = 126
2 x 126 = 252
3 x 126 = 378
4 x 126 = 504
5 x 126 = 630

Calculate how many times the divisor goes in to the digits taken from the dividend, by looking at the multiplication table.
For example:
a) 2 x 37 = 74 and 3 x 37 = 111, so 37 can only go in to 84 twice.
b) 126 goes in to 564 four times.

Write down the number of times the divisor goes in to the digits of the dividend. This is the first digit of the final quotient.
For example:
a) 2
b) 4

Subtract the multiplied divisor from the digits of the dividend to reveal a remainder.
For example:
a) 84  74 = 10
b) 564  504 = 60

Add the last digits of the original dividend to the end of this remainder.
For example:
a) The original dividend was 849, but the 9 was previously disregarded. Now add the 9 on to the end of the remainder, which was 10. This gives you 109.
b) Add the disregarded 2 on to the remainder of 60, giving you 602.

Repeat the process as before, referring to the multiplication table to find out how many times the divisor goes in to the new number.
For example:
a) 37 goes in to 109 twice (74), with a remainder of 35.
b) 126 goes in to 602 four times (504), with a remainder of 98.
These remainders are the final remainders of the sum.

Place the two quotients next to each other to reveal the number of times the divisor goes in to the dividend.
For example:
a)
37 went in to 84 twice, so the quotient is 2.
37 went in to 109 twice, so the quotient is 2.
The final quotient is 22.
b)
126 went in to 564 four times, so the quotient was 4.
126 went in to 602 four times, so the quotient was 4.
The final quotient is 44.

Reveal the final answer and remainder.
For example:
a) 849 ÷ 37 = 22, with a remainder of 35.
b) 5642 ÷ 126 = 44, with a remainder of 98.
Tips & Warnings
 Another simple, but more long winded way to undertake long division is to compile a multiplication table of the divisor, until a number exceeding the dividend is exceeded. Once the maximum number of times the divisor can go in to the dividend is calculated, the closest number which can be achieved by multiplying the divisor, but which is below the dividend, can be subtracted from the dividend to reveal the remainder.
 For example:
 119 ÷ 12
 1 x 12 = 12
 2 x 12 = 24
 3 x 12 = 36
 4 x 12 = 48
 5 x 12 = 60
 6 x 12 = 72
 7 x 12 = 84
 8 x 12 = 96
 9 x 12 = 108
 10 x 12 = 120
 119 108 = 11
 119 ÷ 12 = 9, with a remainder of 11
References
 Photo Credit BananaStock/BananaStock/Getty Images