1. **State the problem:** Find the Highest Common Factor (HCF) of 36 and 108. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leaving a remainder. 3. **Prime factorization:** - 36 = $2^2 \times 3^2$ - 108 = $2^2 \times 3^3$ 4. **Find common factors:** - Common prime factors are $2^2$ and $3^2$ (take the minimum powers). 5. **Calculate HCF:** $$\text{HCF} = 2^2 \times 3^2 = 4 \times 9 = 36$$ 6. **Answer:** The HCF of 36 and 108 is **36**.