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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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