What Are Factors?

A factor is a number that divides exactly into another number with no remainder. Every number has at least two factors: $1$ and itself.

To find factors quickly:

  1. Start with $1$ and the number itself.
  2. Increment from $2$ up to the square root of the number.
  3. Each time a number divides in evenly, record both the divisor and its quotient.

Step-by-Step: Factors of 9

Start with: $$ 1, \quad 9 $$

Try 2:

$$ 9 \div 2 = 4.5 \quad \text{(Not a factor)} $$

Try 3:

$$ 9 \div 3 = 3 \quad \Rightarrow \text{Add } 3 $$

Now we have: $$ 1, \quad 3, \quad 9 $$

No need to test further since: $$ \sqrt{9} = 3 $$

Final Result

The complete set of factors of $9$ is: $$ \boxed{1, 3, 9} $$

Since $9$ has more than two factors, it is a composite number.

✅ The highest factor (excluding 9 itself) is: $$ \boxed{3} $$

Summary

  • Factors are numbers that divide evenly into another number.
  • The factors of $9$ are: $$ 1, \quad 3, \quad 9 $$
  • Because it has more than two factors, $9$ is a composite number.