FI-MO 2010 Problem 2

Determine the least $n\in\mathbb{N}$ such that $n!=1\cdot 2\cdot 3\cdots (n-1)\cdot n$ has at least $2010$ positive factors.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.