For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is $k$.  For example, $S_3$ is the sequence $1,4,7,\ldots$.  For how many values of $k$ does $S_k$ contain $2005$ as a term?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is $k$.  For example, $S_3$ is the sequence $1,4,7,\ldots$.  For how many values of $k$ does $S_k$ contain $2005$ as a term?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is $k$.  For example, $S_3$ is the sequence $1,4,7,\ldots$.  For how many values of $k$ does $S_k$ contain $2005$ as a term?
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