The greatest common divisor, also known as GCD for short, is a term used in mathematics to describe the greatest positive integer that can divide two numbers and result in two more integers. In other words, the greatest integer that results in a non-partial number when dividing two numbers by that integer. The GCD is also known as the greatest common factor, or GCF for short.
There is no quick mathematical formula to calculate the GCD. Instead, an iterative process must be done to calculate the GCD. This iterative process involves starting at the lowest of the two numbers and working down towards 1 to find the greatest number that each integer can be divided by.
Let's say you want to find the GCD of 48 and 18. The iterative process is as follows:
1. Divide 48 by 18 to get a quotient of 2 and a remainder of 12.
2. Divide 18 by 12 to get a quotient of 1 and a remainder of 6.
3. Divide 12 by 6 to get a quotient of 2 and a remainder of 0.
4. Since the remainder is now 0, the GCD is 6.