What mathematical process can be used to determine the GCF?

The greatest common factor (GCF) of a set of numbers is found by identifying the largest factor that the numbers share. Prime factorization is an effective method for this purpose. It involves breaking down each number into its prime factors and then comparing those factors across the numbers.

To find the GCF using prime factorization, you would first express each number as a product of its prime factors. For example, for the numbers 12 and 18, you would find:

• 12 = 2 × 2 × 3 (or (2^2 \times 3))

• 18 = 2 × 3 × 3 (or (2 \times 3^2))

The next step is to identify the common prime factors. In this case, both numbers have the prime factors 2 and 3. The GCF is found by taking the lowest powers of these common factors:

• The lowest power of 2 is (2^1) and for 3, it is (3^1).

Thus, the GCF is (2^1 \times 3^1 = 6). This systematic approach ensures that you accurately determine the GCF, which is