The GCF, or Greatest Common Factor, of 30 and 45 is 15. There are different methods to find the GCF of two numbers, including prime factorization, long division, and Euclidean algorithm. One way to find the GCF of 30 and 45 is to compare the prime factorization of each number. The prime factorization of 30 is 2 x 3 x 5, and the prime factorization of 45 is 3 x 3 x 5. The common prime factors are 3 and 5, so the GCF is 3 x 5 = 15. Another method is to list the factors of each number and find the greatest common factor. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, while the factors of 45 are 1, 3, 5, 9, 15, and 45. The greatest common factor is 15. Therefore, the GCF of 30 and 45 is 15.