Determine the prime factors of 63:
$63$

Step 1 ：$63÷2=31\text{ R }1$

Step 2 ：2 is not a factor of 63.

Step 3 ：$63÷3=21$

Step 4 ：3 is a prime factor of 63.

Step 5 ：$21÷2=10\text{ R }1$

Step 6 ：2 is not a factor of 21.

Step 7 ：$21÷3=7$

Step 8 ：3 is a prime factor of 21.

Step 9 ：$7÷2=3\text{ R }1$

Step 10 ：2 is not a factor of 7.

Step 11 ：7 is a prime number and a prime factor of 63.

Step 12 ：$3\times 3\times 7=63$

Step 13 ：$\boxed{{\displaystyle \text{The prime factors of 63 are 3, 3, and 7.}}}$