A consequence of the Fundamental Theorem of Arithmetic. The book said that:"If $S={1,2,3,.....,200}$, then for each $x \in S$, we may write $x=2^{k}y$, with $k \geq 0$, and gcd(2,y)=1." and the book added that this result follows from the Fundamental Theorem of Arithmetic, but I do not know how?
could anyone explain this for me?   

Write $x$ as a product of primes, where $2$ occurs exactly $k \ge 0$ times, say. Collect together the $k$ occurrences of $2$ to get $x = 2^{k} y$. Clearly $y$ is odd.
