**To find the greatest common factor of two or more integers, the common prime factors of each number are multiplied together.** The result is the greatest common factor of those two or more integers. If there are no common prime factors of the integers, then the greatest common factor is 1.

The simplest way to calculate the greatest common factor of two or more integers involves writing out the prime factors of each number. The common prime factors among the integers are multiplied together, resulting in the greatest common factor.

For example, when determining the greatest common factor between the three integers 12, 38 and 72 the prime factors would be written out for each integer. In this case, the prime factors for 12 are 1, 2 and 3. The prime factors for 38 are 1, 2 and 19. The prime factors of 72 are 1, 2 and 3. The common factors between these three integers are, 1 and 2. These numbers are then multiplied together, equalling 2.

Therefore, 2 is the greatest common factor for 12, 38 and 72. This same process can be executed for more integers as well. Finding the greatest common factor can be helpful when simplifying fractions and performing other mathematical calculations.