The HCF (Highest Common Factor) of a set of 3 coprime numbers is 1.
Understanding Coprime Numbers
Coprime numbers, also known as relatively prime numbers, are numbers that have only 1 as their common factor. This means there's no number (other than 1) that can divide all of them without leaving a remainder.
Why the HCF is 1
Since coprime numbers share no common factors other than 1, the highest common factor they can possibly have is 1. Therefore, by definition, the HCF of any set of coprime numbers will always be 1, regardless of how many numbers are in the set (whether it's 2, 3, or more).
Example
Let's consider the numbers 7, 11, and 13.
- The factors of 7 are 1 and 7.
- The factors of 11 are 1 and 11.
- The factors of 13 are 1 and 13.
The only factor common to all three numbers is 1. Therefore, the HCF(7, 11, 13) = 1.
Conclusion
In summary, if you're dealing with a set of coprime numbers, you can confidently say that their HCF will always be 1. The defining characteristic of coprime numbers is their lack of shared factors beyond the number 1.
