The greatest common factor (GCF) of 42 and 54 is 6. There are different methods to find the GCF of two numbers, but one way is to compare the prime factorization of each number. The prime factorization of 42 is 2 x 3 x 7, and the prime factorization of 54 is 2 x 3 x 3 x 3. The common factors of these two numbers are 2 and 3, and the greatest common factor is the product of these common factors, which is 6. Another method to find the GCF is to list the factors of each number and choose the greatest factor that exactly divides both numbers. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42, and the factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The greatest common factor of 42 and 54 is 6, which is the greatest factor that appears in both lists.