Determine the prime factors of 63:
$63$

Step 1 ：\(63 \div 2 = 31\text{ R }1\)

Step 2 ：2 is not a factor of 63.

Step 3 ：\(63 \div 3 = 21\)

Step 4 ：3 is a prime factor of 63.

Step 5 ：\(21 \div 2 = 10\text{ R }1\)

Step 6 ：2 is not a factor of 21.

Step 7 ：\(21 \div 3 = 7\)

Step 8 ：3 is a prime factor of 21.

Step 9 ：\(7 \div 2 = 3\text{ R }1\)

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 ：\(\boxed{\text{The prime factors of 63 are 3, 3, and 7.}}\)