How many different factors does the integer \(n\) have?

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How many different factors does the integer \(n\) have?

(1) \(n = (a^4)(b^3)\) where \(a\) and \(b\) are different positive prime numbers.
(2) The only positive prime numbers that are factors of \(n\) are \(5\) and \(7.\)

Answer: A

Source: GMAT Prep
Source: — Data Sufficiency |