The number 105840 can be expressed in as 2^4 x 3^3 x 5 x 7^2. Excluding 1 and 105840, how many positive integers are factors of 105840?

Hint: One factor of 105840 can be expressed as 2 x 3^2 x 5 x 7^0
It's a permutation and combination question that is killing me!!!

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