Long Division Calculator
Division is one of the core arithmetic operations, together with multiplication (its inverse), addition and subtraction. These operations let us combine numbers to create new ones. You can view division as counting how many times one number fits into another. For example, 2 fits into 8 four times, so 8 divided by 4 equals 2.
Division can be written in a few different notations. Using the example above:
8 ÷ 4 = 2
8/4 = 2
| = 2 |
In order to more effectively discuss division, it is important to understand the different parts of a division problem.
Components of division
In a typical division problem you deal with three parts: the dividend, the divisor and the quotient. The number that is being split is the dividend, the number that does the splitting is the divisor, and the resulting number is the quotient.
One way to picture the dividend is as the total pool of items available. The divisor represents the number of groups you want to form, and the quotient tells you how many items end up in each group. So, if you have eight people and you want four groups, division shows that each group will contain two people. Sometimes the items cannot be split evenly. In such cases you can either allow a remainder, where the quotient stays an integer and the leftover forms the remainder, or you can continue the division to obtain a decimal. For instance, 9 divided by 4 does not give a whole number; we know that 8 ÷ 4 = 2, so 9 ÷ 4 = 2 R1, meaning 2 with a remainder of 1. Long division lets you find either a quotient with a remainder or an exact decimal value.
How to perform long division?
To carry out long division you first identify the dividend and the divisor. If you want to divide 100 by 7 (100 is the dividend, 7 the divisor), write the dividend underneath the division symbol and place the divisor to the left, then follow the steps below.
| 7 |  | 1 | 0 | 0 |
- Subtract, then bring down the following digit in the original dividend to determine the new dividend.
0 1 7 
1 0 0 7 ↓ 3 0
This is the stopping point if the goal is to find a quotient with a remainder. In this case, the quotient is 014 or 14, and the remainder is 2. Thus, the solution to the division problem is:
This is where you stop if you only need the integer part and a remainder. Here the quotient reads 014 (or simply 14) and the remainder is 2, so the division yields:
To continue the long division problem to find an exact value, continue the same process above, adding a decimal point after the quotient, and adding 0s to form new dividends until an exact solution is found, or until the quotient to a desired number of decimal places is determined.
- Add a decimal point after the quotient and a 0 to the new dividend, and continue the same process as above.
0 1 4 .2 7 1 0 0 7 ↓ 3 0 2 8 2 0 1 4 6