Skill: Identify prime numbers

A prime number is a whole number greater than $1$ that has exactly two positive factors: $1$ and itself.

A number is composite if it has more factors than just $1$ and itself. The number $1$ is neither prime nor composite.

Example: Is $29$ prime?

1. Check that $29$ is greater than $1$.
2. Test whether $29$ is divisible by small prime numbers:
   • It is not divisible by $2$ because it is odd.
   • It is not divisible by $3$ because $2+9=11$, and $11$ is not divisible by $3$.
   • It is not divisible by $5$ because it does not end in $0$ or $5$.
3. Any factor pair of $29$ would need to include a number no greater than $5$, because $6 \times 6=36$, which is greater than $29$.
4. Since $29$ is not divisible by $2$, $3$, or $5$, its only factor pair is

$$1 \times 29.$$

Therefore, $29$ has exactly two positive factors, $1$ and $29$, so $29$ is prime.