Factorization Possibilities

How many different factorizations are there of \[2310 = 2\cdot 3\cdot 5\cdot 7\cdot 11?\]

For instance, the number \(42 = 2\cdot 3\cdot 7\) has five different factorizations: \(42,\ 2\cdot 21,\ 3\cdot 14,\ 6\cdot 7,\ 2\cdot 3\cdot 7\).

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