2. (10 points) Determine how many prime divisors the number 17! - 15! has (here $n!=1 \cdot 2 \cdots n-$ is the factorial of the number $n$, i.e., the product of all natural numbers from 1 to n inclusive).
a) 6 ;

b) 7 ;

c) 8 ;

d) none of the listed answers is correct.

Mark the correct answer, no need to provide the solution.
Answer: b).

Solution. Transform: $17!-15!=15!(16 \cdot 17-1)=15! \cdot 271$. The prime divisors of this number are $2,3,5,7,11,13,271$.