2005 iTest Problems/Problem 4

Taking one factor of $2005$ as a base, the other is split into $5 ^1 \cot{ 401 ^1} = 2005$ . This means $2005$ has $(1 + 1)\cdot{(1 + 1)} = 4$ divisors. Each of these divisors represents a multiple of $2005$ , meaning the answer is $\boxed{4}$