Problem 1: Consider the fundamental theorem of arithmetic, which is stated as follows: Every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes, where the prime factors are written in order of nondecreasing size. We want to use a stack to read a number and print all of its prime divisors in descending order. For example, with the integer 2100, the output should be:

7 5 5 3 2 2 1.

Write a procedure in our algorithmic language, called Prime_Factorization, which accepts a positive integer greater than 1, and generates its prime factorization according to the above-mentioned theorem. [Hint: The smallest divisor greater than 1 of any integer is guaranteed to be a prime.]

2. Propose a stack class to accommodate this prime decomposition. It should have at least two member functions: One to compute the prime factorization of an integer, and one to print all corresponding prime divisors in descending order.