For this assignment, you will write a C program that calculates and displays the prime factorization of any integer greater than 1.

Requirements:

Your program must compile and run correctly using the gcc compiler on ale.

Your program must prompt the user for an integer greater than 1, and then display its prime factorization in the format used in the Sample Runs below.

Your program must check that the number entered is, in fact, a positive integer. If it is not, your program should re-prompt until a positive integer is entered. The program need not check, however, whether the user entered an integer in the first place.

Your program must show the prime factorization as only the product of the prime factors whose factor power is greater than 0.

Your program must include both the prototype and definition of a function called factor_power(), which takes two integer parameters, n and d, and returns the unique non-negative integer p, such that d raised to the p power divides n but d raised to the (p+1) power does not divide n.

Sample Runs:

% ./factor

Enter an integer (> 1): -1

Enter an integer (> 1): 1

Enter an integer (> 1): 1200

1200 = 2^4 * 3^1 * 5^2

% ./factor

Enter an integer (> 1): 17

17 = 17^1

% ./factor

Enter an integer (> 1): 123456789

123456789 = 3^2 * 3607^1 * 3803^1

Notes on mathematics:

A factor of a positive integer n is an integer which evenly divides n; that is, one which leaves no remainder when n is divided by it. Thus 2, 3, 4, and 6 are all factors of 12, but 5 is not, as 12 divided by 5 has a remainder of 2. We can test whether one number is a factor of another using the modulus (%) operator, which returns the remainder from integer division. Thus 12%5 is 2, while 12%6 is 0. Every number is a factor of itself, and 1 is a factor of every number.

A prime number is a positive integer which is greater than 1 whose only factors are 1 and itself. Thus 17 is a prime number, whereas 12 is not.

The prime factorization of a positive integer n is the unique list of prime numbers which when multiplied together result in n. Thus the prime factorization of 12 is 2^2 * 3^1, while that of 625 is 5^4.

Note: we write 2^2 instead of 2 * 2, and 3^1 instead of 3, and 5^4 instead of 5 * 5 * 5 * 5.