Evaluate \( \gcd ( 19 ! + 19, 20! + 19 ) \).

**Details and assumptions**

The number \( n!\), read as **n factorial**, is equal to the product of all positive integers less than or equal to \(n\). For example, \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).

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