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n! has at least 2010 factors

Source: Finnish Mathematics Competition 2010, Final Round, Problem 2

November 15, 2011
number theory unsolvednumber theory

Problem Statement

Determine the least n∈Nn\in\mathbb{N} such that n!=1⋅2⋅3⋯(n−1)⋅nn!=1\cdot 2\cdot 3\cdots (n-1)\cdot n has at least 20102010 positive factors.
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