The Greatest common divisor (GCD) of two or more numbers is the largest number that divides evenly into each of the numbers. The process of finding the GCD is to find the largest number that divides evenly into each of the numbers, and then keep dividing that number until there is no remainder.
For example, the GCD of 8 and 12 is 4, because 4 is the largest number that divides evenly into 8 and 12. 8 can be divided evenly by 4 and 12 can be divided evenly by 4, so 4 is the GCD. Another example is the GCD of 15 and 21. The largest number that divides evenly into 15 and 21 is 15, so 15 is the GCD.
Example 1: The GCD of 12 and 18 is 6. 12 divided by 6 is 2 with a remainder of 0, 18 divided by 6 is 3 with a remainder of 0, so 6 is the GCD.
 | = | least common multiple |
 | = | greatest common divisor |
 | = | non-zero integers |
Example 2: The GCD of 15 and 30 is 5. 15 divided by 5 is 3 with a remainder of 0, 30 divided by 5 is 6 with a remainder of 0, so 5 is the GCD.