As $n$ ranges over the positive integers, what is the maximum possible value that the greatest common divisor of $13n + 8$ and $5n+3$ can take?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
As $n$ ranges over the positive integers, what is the maximum possible value that the greatest common divisor of $13n + 8$ and $5n+3$ can take?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
As $n$ ranges over the positive integers, what is the maximum possible value that the greatest common divisor of $13n + 8$ and $5n+3$ can take?
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