To factor the expression $16a + 8$, we begin by identifying the greatest common factor (GCF) and then factoring it out.

First, we determine the GCF of the terms $16a$ and $8$. The GCF is the largest integer that evenly divides both terms. In this case, the GCF of $16$ and $8$ is $8$.

Next, we can express each term as a product involving the GCF. For the term $16a$, we can rewrite it as $8 \cdot 2a$. For the term $8$, we can express it as $8 \cdot 1$.

Now, we factor out the GCF from both terms. This means we take $8$ out of each term and place it outside a set of parentheses. Inside the parentheses, we include the remaining factors. Thus, the expression $16a + 8$ can be factored as follows:

Therefore, the factorized form of $16a + 8$ is $8(2a + 1)$. This method of factorization, which involves finding the GCF and using it to simplify the expression, is a fundamental skill in algebra that aids in solving equations and simplifying expressions effectively.