The greatest common factor (GCF) of 81 and 72 is 9. One way to find the GCF of two numbers is to compare their prime factorizations. The prime factorization of 81 is 3 x 3 x 3 x 3, while the prime factorization of 72 is 2 x 2 x 2 x 3 x 3. The common factors are 3 and 3, so the GCF is 3 x 3 = 9. Another method to find the GCF is to list the factors of each number and find the greatest common factor. The factors of 81 are 1, 3, 9, 27, and 81, while the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The common factors are 1, 3, 9, and the greatest common factor is 9.