For the trial division factorization, for a positive integer $n$, I know that the number of divisions by all primes in the range $1$ to $\sqrt{n}$ is approximately (using prime number theorem) $2\times\frac{\sqrt{n}}{\ln n}=O\left(\frac{\sqrt{n}}{\ln n}\right)$ and the number of divisions by all the integers in the range $1$ to $\sqrt{n}$ is $\sqrt{n}=O(\sqrt{n})$.
I am asked to evaluate these expressions for $n=7^{76}$ and $n=11^{111}$ and then compare their orders of magnitude using the big $O$ notation. What do I have to do for the latter part? I simply do not understand what "compare their orders of magnitude using the big $O$ notation" means?