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

To find factors of a number like $63$, follow this simple method:

  • Begin with $1$ (since $1$ divides every integer).
  • Check sequentially whether each number divides $63$ evenly.
  • If it does, add both the divisor and its quotient to your list.
  • Stop once you reach $\sqrt{63}$.

Step-by-Step: Factors of 63

We start by noting: $$ \text{Initial factors: } 1, \ 63 $$

Try 2:

$$ 63 \div 2 = 31.5 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 3:

$$ 63 \div 3 = 21 \quad \Rightarrow \text{Add } 3, \ 21 $$

Try 4:

$$ 63 \div 4 = 15.75 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 5:

$$ 63 \div 5 = 12.6 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 6:

$$ 63 \div 6 = 10.5 \quad \text{(Not exact)} \quad \Rightarrow \text{Skip} $$

Try 7:

$$ 63 \div 7 = 9 \quad \Rightarrow \text{Add } 7, \ 9 $$

Now that we’ve reached $\sqrt{63} \approx 7.94$, we stop checking.

All Factors of 63

The full list of factors is: $$ 1, \ 3, \ 7, \ 9, \ 21, \ 63 $$

Since there are more than two factors, $63$ is a composite number.

✅ The highest factor (excluding $63$ itself) is: $$ \boxed{21} $$

Summary

  • Factors are numbers that divide exactly into a given number.
  • Prime numbers have exactly two factors: $1$ and itself.
  • Composite numbers have more than two factors.
  • The factors of $63$ are: $$ 1, \ 3, \ 7, \ 9, \ 21, \ 63 $$
  • So $63$ is a composite number.