The highest common factor (HCF), also known as the greatest common divisor (GCD), of two prime numbers is always 1.
Prime numbers are defined as numbers greater than 1 that have no divisors other than 1 and themselves. For example, the numbers 2, 3, 5, 7, 11, and 13 are all prime. When you take any two distinct prime numbers, they will not share any common factors apart from 1. This is because the only factors of each prime number are 1 and the number itself.
For instance, if we take the prime numbers 5 and 7, the factors are as follows:
- Factors of 5: 1, 5
- Factors of 7: 1, 7
The only common factor between them is 1, hence the HCF is 1. This holds true for any pair of distinct prime numbers.