#### Answer

$2w$

#### Work Step by Step

In order to find the GCF of a set of terms, we list the prime factors of each of the terms, figure out which prime factors are shared by all of the terms, and then multiply the shared factors:
The prime factors of $8w^2$ are $2\times2\times2\times w\times w$
The prime factors of $18w$ are $2\times3\times3\times w$
The common prime factors are $2\times w$, which equals $2w$, so this is the GCF of the terms.