The highest common factor (HCF) is the largest number that can divide two or more numbers without leaving a remainder. When we say that the HCF of two numbers is 1, it indicates that these two numbers are coprime, which means they have no common factors other than 1.
For example, consider the numbers 8 and 15. The factors of 8 are 1, 2, 4, and 8, while the factors of 15 are 1, 3, 5, and 15. The only common factor between them is 1, making their HCF equal to 1, thereby indicating that they are coprime.
There are countless pairs of numbers that can have an HCF of 1. Here are a few examples:
- 5 and 9
- 14 and 25
- 21 and 40
- 7 and 18
- 17 and 34
It’s interesting to note that any prime number will be coprime with any other number that is not its multiple. For example, the prime number 3 will be coprime with 10, 11, or 14, as none of these numbers share any factors with 3 other than 1.
In summary, when two numbers have an HCF of 1, they can be any pair of integers that do not share any other common factors, leading to a wide variety of possible combinations.