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

To find the factors of a number:

  1. Start with $1$ and the number itself.
  2. Try dividing the number by increasing integers.
  3. If there is no remainder, add both the divisor and quotient to your factor list.
  4. Stop testing once you pass the square root of the number.

Step-by-Step: Factors of 25

Begin with: $$ 1, \quad 25 $$

Try 2:

$$ 25 \div 2 = 12.5 \quad \text{(Not exact)} $$

Try 3:

$$ 25 \div 3 \approx 8.33 \quad \text{(Not exact)} $$

Try 4:

$$ 25 \div 4 = 6.25 \quad \text{(Not exact)} $$

Try 5:

$$ 25 \div 5 = 5 \quad \Rightarrow \text{Add } 5 $$

You now have all the factors: $$ 1, \quad 5, \quad 25 $$

We stop here since: $$ \sqrt{25} = 5 $$


Final Result

The full list of factors of $25$ is: $$ 1, \quad 5, \quad 25 $$

Since $25$ has more than two factors, it is a composite number.

✅ The highest factor other than the number itself is: $$ \boxed{5} $$


Summary

  • A factor divides evenly into a number.
  • The factors of $25$ are: $$ 1, \quad 5, \quad 25 $$
  • Since 25 has more than two factors, it is a composite number, not a prime number.