Question on number theory.

I solved 250 Thousand Tons of TNT and I took a look at the solution to see if there was a better way to do it.

I am confused about the first proposal: "Since $$$k$$$ is a divisor of $$$n$$$, there are $$$\mathcal{O}(\sqrt[3]{n})$$$ such $$$k$$$."

I know that you can find the number of divisors of an integer $$$n$$$ in $$$\mathcal{O}(\sqrt[3]{n})$$$ but I don't think that's an upper bound for the amount of divisors itself.

Am I missing something? Have I misunderstood the explanation?