Skill: Determine whether a number is prime

A number is prime if it is greater than $1$ and has exactly two positive factors: $1$ and itself. If it has more factors, it is composite. The number $1$ is neither prime nor composite.

To decide, look for a multiplication pair that makes the number. If you find a pair other than $1$ and the number itself, the number is composite. If no other pair works, it is prime.

Example: Is $(17)$ prime?

1. $(17)$ is greater than $1$, so it could be prime.
2. Check whether $(17)$ can be divided evenly by numbers other than $1$ and $(17)$.
   • It is not even, so $2$ is not a factor.
   • $(3 \times 5=15)$ and $(3 \times 6=18)$, so $3$ is not a factor.
   • $(4 \times 4=16)$ and $(4 \times 5=20)$, so $4$ is not a factor.
3. Any multiplication pair using $5$ or a larger number would need another factor of $4$ or less to make $(17)$. Those possibilities have already been checked.
4. The only factor pair is

$$1 \times 17=17.$$

Therefore, $(17)$ has exactly two positive factors, $1$ and $(17)$, so $(17)$ is prime.