List the factors of each number
Find the factors they have in common
Choose the greatest factor they share
Use prime factorization to break each number into primes
Identify the prime factors both numbers share
Multiply the shared prime factors
Use the Euclidean algorithm for larger numbers
Divide the larger number by the smaller number
Replace the larger number with the remainder
Repeat until the remainder is 0
The last nonzero remainder is the greatest common factor