Find It Without Plugging Values

Number Theory Level 1

$\large n! + 1 \qquad \qquad (n+1)! + 1$

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

Notation: $!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .