A factor is a number that divides into another number without leaving a remainder.

To find the factors of a number like $64$:

  • Start from $1$ and test incrementally.
  • For each divisor that divides evenly, include both the divisor and its quotient.
  • Stop once the divisor exceeds $\sqrt{64}$.

Step-by-Step: Factors of 64

We begin with:

$$ \text{Initial factors: } 1, \ 64 $$

Try 2:

$$ 64 \div 2 = 32 \quad \Rightarrow \text{Add } 2 \text{ and } 32 $$

Try 3:

$$ 64 \div 3 \approx 21.33 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 4:

$$ 64 \div 4 = 16 \quad \Rightarrow \text{Add } 4 \text{ and } 16 $$

Try 5:

$$ 64 \div 5 = 12.8 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 6:

$$ 64 \div 6 \approx 10.67 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 7:

$$ 64 \div 7 \approx 9.14 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

We stop here, since:

$$ \sqrt{64} = 8 $$

We know that $8$ divides exactly:

$$ 64 \div 8 = 8 \quad \Rightarrow \text{Add } 8 $$

All Factors of 64

The complete list of factors is: $$ 1, \ 2, \ 4, \ 8, \ 16, \ 32, \ 64 $$

Since $64$ has more than two factors, it is a composite number.

✅ The highest factor (excluding $64$ itself) is: $$ \boxed{32} $$

Summary

  • A factor divides a number exactly with no remainder.
  • A prime number has exactly two factors: $1$ and itself.
  • A composite number has more than two factors.
  • The number $64$ is composite, and its factors are: $$ 1, \ 2, \ 4, \ 8, \ 16, \ 32, \ 64 $$