Co-prime numbers, also known as relatively prime numbers, are two or more integers that have no common factors other than 1. In other words, the greatest common divisor (GCD) of these numbers is 1. To determine if a set of numbers are co-prime, you can take the following steps:
- Identify the numbers you want to check.
- Calculate the GCD of the numbers using the Euclidean algorithm or by listing out the factors.
- If the GCD is 1, the numbers are co-prime. If it is greater than 1, they are not co-prime.
For example, let’s consider the numbers 8 and 15:
- Factors of 8: 1, 2, 4, 8
- Factors of 15: 1, 3, 5, 15
The only common factor is 1, so 8 and 15 are co-prime.
On the other hand, if we check 8 and 12:
- Factors of 8: 1, 2, 4, 8
- Factors of 12: 1, 2, 3, 4, 6, 12
Here, 8 and 12 share common factors (1, 2, 4), hence they are not co-prime.
So, to determine whether a set of numbers is co-prime, calculate their GCD and check if it equals 1.