What Are Factors?

A factor of a number is any number that divides into it exactly—without leaving a remainder. Factors are always less than or equal to the original number.

To find the factors of a number:

  1. Start with $1$ and the number itself.
  2. Test numbers sequentially starting from $2$.
  3. If the number divides evenly (no remainder), add both the divisor and the quotient to your factor list.
  4. Stop once you’ve passed the square root of the number.

Step-by-Step: Factors of 15

Start with: $$ 1, \quad 15 $$

Try 2:

$$ 15 \div 2 = 7.5 \quad \text{(Not a factor)} $$

Try 3:

$$ 15 \div 3 = 5 \quad \Rightarrow \text{Add } 3 \text{ and } 5 $$

At this point, we have: $$ 1, \quad 3, \quad 5, \quad 15 $$

No need to go further since: $$ \sqrt{15} \approx 3.87 $$

Final Result

The full list of factors of $15$ is: $$ \boxed{1, 3, 5, 15} $$

Since $15$ has more than two factors, it is a composite number.

✅ The highest factor other than $15$ is: $$ \boxed{5} $$

Summary

  • Factors are numbers that divide evenly into another number.
  • The factors of $15$ are: $$ 1, \quad 3, \quad 5, \quad 15 $$
  • $15$ is a composite number because it has more than two factors.