\[ \large n! + 1 \qquad \qquad (n+1)! + 1 \]

If \(n\) is a positive integer, find the greatest common divisor of the two numbers above.

\[\]**Notation**: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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