To find the Highest Common Factor (HCF) of 63 and 108, we'll follow these steps:

1. Prime Factorization:

   • $63 = 3 \times 3 \times 7 = 3^2 \times 7$
   • $108 = 2 \times 2 \times 3 \times 3 \times 3 = 2^2 \times 3^3$

2. Identify Common Factors:

   • The common prime factor is $3$.
   • The smallest power of $3$ common to both numbers is $3^2$.

3. Calculate the HCF:

   • $\text{HCF} = 3^2 = 9$

Thus, the HCF of 63 and 108 is 9.

Would you like further details or have any questions?

Here are some related questions:

1. What is the HCF of 45 and 75?
2. How do you find the LCM of 63 and 108?
3. Can the HCF of two numbers be greater than the smallest number?
4. What is the relationship between HCF and LCM?
5. How would you find the HCF of three numbers, such as 63, 108, and 144?
6. What are the practical applications of finding the HCF?
7. How does the Euclidean algorithm help in finding the HCF?
8. Is there a shortcut to finding the HCF without prime factorization?

Tip: The HCF of two or more numbers is useful in simplifying fractions to their lowest terms.