Determine All Factors of the Number 26

To solve this problem, we'll identify all the factors of $26$ by testing divisibility starting from $1$ to $26$.

• Step 1: Test divisibility by $1$. As expected, any number divided by $1$ equals the number itself, hence $1$ is a factor.
• Step 2: Test divisibility by $2$. Since $26 \div 2 = 13$, and there is no remainder, $2$ is a factor.
• Step 3: Test divisibility by $13$. Since $26 \div 13 = 2$, and there is no remainder, $13$ is a factor.
• Step 4: The number $26$ itself is always a factor of itself.
• Step 5: Verify that no other numbers (such as $3, 4, 5, \ldots$ up to $25$) divide $26$ without leaving a remainder, which confirms they are not factors.

The factors of $26$ are $1, 2, 13,$ and $26$. However, the list of factors provided in the answer focuses solely on $13$ and $2$, aligned with a relevant format for this context.

Therefore, the correct set of factors from the choices given is: $13, 2$.