Final answer:
The greatest common factor of 19 and 18 is 1 since 19 is a prime number and has no other factors that divide 18.
Step-by-step explanation:
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 19 and 18, we need to determine the factors of both numbers. Since 19 is a prime number, its only factors are 1 and itself (19).
The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 19 and 18 are therefore just 1, as 19 has no other factors. Hence, the greatest common factor of 19 and 18 is 1.