1. **Problem Statement:** We are given two co-prime numbers whose product is 553. We need to find their Highest Common Factor (HCF). 2. **Key Concept:** Two numbers are co-prime if their HCF (or GCD) is 1. 3. **Given:** Product of two co-prime numbers = 553 4. **Since the numbers are co-prime, their HCF = 1.** 5. **Answer:** The HCF of two co-prime numbers is always 1. Therefore, the correct option is (a) 1.