The greatest common factor (GCF) of two numbers is the largest positive integer that divides both numbers without leaving a remainder.
In the case of 19 and 13, both numbers are prime. The only positive integer that divides both 19 and 13 is 1. Therefore, the greatest common factor of 19 and 13 is:
\[ \text{GCF}(19, 13) = 1 \]