The greatest common factor (GCF) of 9 and 36 is 9. One way to find the GCF of two numbers is to compare their prime factorizations. The prime factorization of 9 is 3 x 3, and the prime factorization of 36 is 2 x 2 x 3 x 3. The common prime factors are 3 and 3, so the GCF is 3 x 3 = 9. Another way to find the GCF is to list the factors of each number and find the greatest common factor. The factors of 9 are 1, 3, and 9, and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The greatest common factor of 9 and 36 is 9 because it is the largest number that divides both 9 and 36 without a remainder.