Final answer:
To find the value of n that needs to be listed as a prime factor of B so that the greatest common factor (GCF) of A and B is 9, we need to examine the prime factorizations of A and B and identify the common prime factors with an exponent of at least 2.
Step-by-step explanation:
To find the value of n that needs to be listed as a prime factor of B so that the greatest common factor (GCF) of A and B is 9, we need to examine the prime factorizations of A and B. Let's assume the prime factorization of A is 3^2 * 2^3 * 5^4 and the prime factorization of B is 3^n * 7^2 * 5^3. Since the GCF is 9, it means that the common prime factors between A and B should have an exponent of at least 2, which is the exponent for 3 in the prime factorization of 9. Therefore, we need to choose n = 2 to get the GCF of 9.