The HCF (Highest Common Factor), also known as the GCD (Greatest Common Divisor), of two prime numbers is always 1.
Explanation
Prime numbers are whole numbers greater than 1 that have only two factors: 1 and themselves. When considering two distinct prime numbers, their only common factor will invariably be 1. This is because prime numbers, by definition, are not divisible by any number other than 1 and themselves. Since they are distinct primes, they won't share "themselves" as a common factor.
For example, let's consider the prime numbers 7 and 11.
- Factors of 7: 1, 7
- Factors of 11: 1, 11
The only common factor they share is 1.
Co-prime Numbers
Numbers that have only 1 as their common factor are also known as co-prime or relatively prime numbers. Two prime numbers are, by definition, co-prime.
Example
Let's take another example with the prime numbers 2 and 3.
- Factors of 2: 1, 2
- Factors of 3: 1, 3
Again, the highest common factor is 1.
Therefore, no matter which two prime numbers you choose, their highest common factor will always be 1.
