The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a product of primes." The fact that this breakdown always results in the same primes is viewed as "obvious." The purpose of this paper is to illustrate with a number of examples that the "Unique Factorization Property" is a rare property and the fact that the natural numbers possess this property is "fundamental" to our understanding of this number system.