1. **Problem Statement:** Given that $p$ and $q$ are natural numbers and $p$ is a multiple of $q$, find the Highest Common Factor (HCF) of $p$ and $q$. 2. **Understanding the problem:** If $p$ is a multiple of $q$, it means there exists some natural number $k$ such that: $$p = k \times q$$ 3. **Formula for HCF:** The HCF of two numbers is the greatest number that divides both without leaving a remainder. 4. **Applying the condition:** Since $p = kq$, every divisor of $q$ also divides $p$. The largest such divisor is $q$ itself. 5. **Conclusion:** Therefore, the HCF of $p$ and $q$ is: $$\boxed{q}$$ This corresponds to option (c).