Data Sufficiency

For any integer \(n\) greater than \(1,\) factorial denotes the product of all the integers from \(1\) to \(n,\) inclusive. It’s given that \(a\) and \(b\) are two positive integers such that \(b>a.\) What is the total number of factors of the largest number that divides the factorials of both \(a\) and \(b?\)

(1) \(a\) is the greatest integer for which \(3^a\) is a factor of product of integers from \(1\) to \(20,\) inclusive.

(2) \(b\) is the largest possible number that divides positive integer \(n,\) where \(n^3\) is divisible by \(96.\)

Answer: A

Source: e-GMAT