Factorization Possibilities

Discrete Mathematics Level 3

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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