basic/low level c++ please include comments

Fundamental Theorem of Arithmetic The fundamental theorem of arithmetic states Every positive integer greater than 1 can be represented as an unique (ignoring ordering) prime factorization (product of primes) Create a program that is a prime factorization calculator for integers between 2 and 1000. The program should prompt the user to enter a positive number greater than 1, and then, t displays the prime factorization of the number in ascending order in exponential form. For example, if the user entered 56, the program should display 56= (2^3)(7-1) . Furthermore, the program should continue to prompt the user until the user enters 0. Your program must o generate the prime numbers; it cannot just read the numbers from a file o have at least three functions excluding the main function o, not include prime numbers with zero powers in the prime factorization of the input of the user Once you finish with your program, use the program to help answer the following questions If (n) equals the sum of n's factors and (n) equals the count of n,s factors, then (a) if n-p is prime, what is (n) and (n)? (b) if n = pq where p and q are both prime, what is (n) and (n)? (c) if n-pm where p is prime and m > 1, what is (n) and T(n)? For extra credit, create a file that lists the prime factorization of all the numbers between 2 and 1000. in ascending order