Say a>1 is natural co-prime, hence a=b*c, when 1<b,c<a. Suppose that b<=c ==> b^2<=bc=a or b<=sqrt(a). b>1 therefor b have at least one prime factor, say p; hence p<=b<=sqrt(a), moreover p|b. and b|a, hence p|a...

So we can conclude that for co-prime a, must to be prime factor p, when p<=sqrt(a)