List the factors of each number
Identify the factors they have in common
Choose the greatest factor that appears in every list
If using prime factorization, write each number as a product of primes
Find the prime factors shared by all numbers
Multiply the shared prime factors
If using the Euclidean algorithm, divide the larger number by the smaller number
Replace the larger number with the smaller number and the smaller number with the remainder
Repeat until the remainder is 0
The last nonzero remainder is the GCF