The easiest way (in my opinion) is to draw a factor tree. Let's take 4400 as an example. 4400 factors as . So you would draw two lines extending from 4400 with 44 and 100 at the end of each. Now 44 can be factored as . So do the same thing with 2 lines extending from 44 with 4 and 11 at the ends. Circle the number 11 because it is prime. Similarly from 4 draw 2 lines and put 2 at the end of each. Circle these because they're prime. You still have to draw some more branches from 100 - can you finish on your own?
In the end, write all the circled numbers in increasing order. This is the prime factorization in canonical form (canonical is just a fancy word for "natural").
(Perhaps someone with better latex skills than me can actually draw the tree)