Factorization

Do you remember writing whole numbers as products of primes? For example,

$$12=2\times 2\times 3.$$

Can this sort of thing always be done? Is it really hard or really easy? For example, is factoring social security numbers ``trivial'' or hopeless? In fact, it's trivial; even my wristwatch can do it!! (Mine might be the only wristwatch in the world that can factor social security numbers, but that's another story.) What about bigger numbers?

These questions are important to your everyday life. If somebody out there secretly knows how to factor $200$-digit numbers quickly, then that person could easily read you credit card number and expiration date when you send it to amazon.com.