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:

\[42,\ \ 2\times 21,\ \ 3\times 14,\ \ 6\times 7,\ \ 2\times 3\times 7.\]

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