The greatest common factor (GCF) of 36 and 60 is 12. There are several methods to find the GCF of two numbers, including listing common factors, prime factorization, and the Euclidean algorithm. One way to find the GCF of 36 and 60 is to list their common factors: 1, 2, 3, 4, 6, and 12. Since 12 is the greatest common factor, it is the answer. Another way to find the GCF is to compare the prime factorization of each number. The prime factorization of 36 is 2 x 2 x 3 x 3, and the prime factorization of 60 is 2 x 2 x 3 x 5. The common prime factors are 2, 2, and 3. Multiplying these together gives 12, which is the GCF. The Euclidean algorithm is a more complicated method for finding the GCF, but it can also be used.