Prove that if integer n>=2 is composite, then n has a prime divisor which is <=(n)^1/2

My first thought was to somehow use the fundamental theorem of arithmetic.

I have n=p1p2...pr.

I assumed each integer >=2 can be factored into primes.

Then assuming k+1 is composite, we have k+1=ab where 2<=a,k+1 and 2<=b<k+1. But at this step I get stuck.