Skill: Determine whether a number is composite

A whole number greater than $1$ is composite if it has more than two positive factors. A quick way to check is to find a factor pair: two whole numbers greater than $1$ that multiply to make the number.

Example: Is $18$ composite?

1. Look for two whole numbers that multiply to $18$.

$$2 \times 9 = 18$$

2. The factors $2$ and $9$ are both smaller than $18$, so this is a nontrivial factor pair.

3. Therefore, $18$ can be arranged into a rectangle with $2$ rows and $9$ columns. It has more than one factor pair:

$$1 \times 18 \quad \text{and} \quad 2 \times 9$$

4. Since $18$ has more than two positive factors, it is composite.

Remember: A number with exactly two positive factors is prime, and $1$ is neither prime nor composite.