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

To find factors quickly:

  1. Start with $1$ and the number itself.
  2. Increment the divisor and check: Does it divide the number exactly?
  3. If yes, add both the divisor and the quotient.
  4. Stop when the divisor exceeds the square root of the number.

Step-by-Step: Factors of 28

Start with: $$ 1, \quad 28 $$

Try 2:

$$ 28 \div 2 = 14 \quad \Rightarrow \text{Add } 2 \text{ and } 14 $$ Factor list: $1, 2, 14, 28$

Try 3:

$$ 28 \div 3 \approx 9.33 \quad \text{Not exact} $$

Try 4:

$$ 28 \div 4 = 7 \quad \Rightarrow \text{Add } 4 \text{ and } 7 $$ Factor list: $1, 2, 4, 7, 14, 28$

Try 5:

$$ 28 \div 5 = 5.6 \quad \text{Not exact} $$

Now that you’ve passed $\sqrt{28} \approx 5.29$, you can stop.

Final List of Factors

The complete list of factors of $28$ is: $$ 1, \quad 2, \quad 4, \quad 7, \quad 14, \quad 28 $$

Since 28 has more than two factors, it is a composite number.

✅ The highest factor other than 28 is: $$ \boxed{14} $$

Summary

  • A factor divides a number without a remainder.
  • The factors of $28$ are: $$ 1, \quad 2, \quad 4, \quad 7, \quad 14, \quad 28 $$
  • Because 28 has more than two factors, it is classified as a composite number, not a prime number.