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

To find the factors of a number quickly:

  1. Start at $1$ — which divides every whole number.
  2. Increment your divisor and ask: Does this divide the number exactly?
  3. If yes, record both the divisor and its quotient.
  4. Stop once you reach or exceed the square root of the number.

Step-by-Step: Factors of 45

Begin with: $$ 1, \quad 45 $$

Try 2:

$$ 45 \div 2 = 22.5 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 3:

$$ 45 \div 3 = 15 \quad \text{✓ Add } 3 \text{ and } 15 $$

Updated list: $$ 1, \quad 3, \quad 15, \quad 45 $$

Try 4:

$$ 45 \div 4 = 11.25 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 5:

$$ 45 \div 5 = 9 \quad \text{✓ Add } 5 \text{ and } 9 $$

Updated list: $$ 1, \quad 3, \quad 5, \quad 9, \quad 15, \quad 45 $$

Try 6:

$$ 45 \div 6 = 7.5 \quad \text{Not exact} \Rightarrow \text{Stop} $$

You’ve now reached $\sqrt{45} \approx 6.7$, so no more checks are needed.

All Factors of 45

The complete list of factors: $$ 1, \quad 3, \quad 5, \quad 9, \quad 15, \quad 45 $$

Since there are more than two factors, $45$ is a composite number.

✅ The highest proper factor is: $$ \boxed{15} $$

Summary

  • Factors divide a number exactly with no remainder.
  • The factors of $45$ are: $$ 1, \quad 3, \quad 5, \quad 9, \quad 15, \quad 45 $$
  • Because it has more than two factors, $45$ is a composite number, not prime.