Let $d = \gcd(n + 7, 2n + 1)$, so $d$ divides both $n + 7$ and $2n + 1$.  Then $d$ divides $2(n + 7) - (2n + 1) = 13$, so $d$ is at most 13.

If $n = 6$, then $\gcd(n + 7, 2n + 1) = \gcd(13,13) = 13$, which shows that the value of 13 is attainable.  Therefore, the greatest possible value of $\gcd(n + 7, 2n + 1)$ is $\boxed{13}$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $n$ be a positive integer.  What is the greatest possible value of $\gcd(n + 7, 2n + 1)$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
13
Let $n$ be a positive integer.  What is the greatest possible value of $\gcd(n + 7, 2n + 1)$?
test