No, it is not possible for a composite number to have more than one prime factorization. Example- Consider 6. Then there are two factorization. 6 = 2*3 and 6 = 1*6. And from both the factorizations,6 = 2*3 is a prime factorizations and 6 = 1*6 is not a prime factorization because, 6 is not a prime number. Thus, only 1 prime factorization is possible.