Factors are numbers that divide evenly into another number without leaving a remainder. A factor can never be greater than the original number.

To find the factors of a number quickly:

  1. Start with $1$ and the number itself.
  2. Try dividing the number by each integer from $2$ upwards.
  3. If the division leaves no remainder, add both the divisor and quotient to the factor list.
  4. Stop once the divisor exceeds $\sqrt{n}$.

Step-by-Step: Factors of 27

We start with: $$ 1, \quad 27 $$

Try 2:

$$ 27 \div 2 = 13.5 \quad \text{(Not exact)} $$

Try 3:

$$ 27 \div 3 = 9 \quad \Rightarrow \text{Add } 3 \text{ and } 9 $$ Factor list: $1, 3, 9, 27$

Try 4:

$$ 27 \div 4 = 6.75 \quad \text{(Not exact)} $$

Try 5:

$$ 27 \div 5 = 5.4 \quad \text{(Not exact)} $$

We stop here since: $$ \sqrt{27} \approx 5.2 $$

Final List of Factors

The complete set of factors of $27$ is: $$ 1, \quad 3, \quad 9, \quad 27 $$

Since 27 has more than two factors, it is a composite number.

✅ The highest factor other than 27 is: $$ \boxed{9} $$

Summary

  • A factor divides a number with no remainder.
  • The factors of $27$ are: $$ 1, \quad 3, \quad 9, \quad 27 $$
  • Since 27 has more than two factors, it is a composite number, not a prime number.