C Programming Homework #3: Prime Factorization

Due: Monday, February 8, 2016

This week continue reading in Lesson #6, Lesson #7, and Lesson #8. This is the same reading as for last week. Lesson #9 contains useful information on while loops and compound conditions. Some of that material in that lesson we'll cover next week.

Using the prime number checking program as a basis, write a program that prints the prime factorization of a given number. The prime factorization of N is the (unique) set of primes that when all multiplied together give N. Some of the primes might be repeated. For example the prime factorization of 12 is 2*2*3. The prime factorization of 100 is 2*2*5*5.

To do this, find the first prime factor of N (the first factor is definitely prime so you don't need to check for primality) and print it. Then divide N by the factor found and repeat (you might find a while loop useful. You can print each factor on a line by itself.
For the final version of this program, count the number of times each factor occurs and print that number with each factor. For example, given 100 output:
```
  2^2
  5^2
```

Submit your program to Moodle (the .c file). Be sure it includes a comment block at the top that includes your name, the name of the file, the date, and a brief description of what the program does..