I understand this is intuitively obvious. I am wondering if there is a axiom or principle or proof that shows this? It seems you may need something that says you can decompose an integer into it's lowest common factors and if a number is odd then each of it's lowest common factors will never be divisible by two which is the lowest possible even integer. 

It seems like there may be something fundamental beside my intuition here in number theory maybe...and that I either forgot or never learned.