which positive integers less than 12 are relatively prime to 13
Since 13 has no factors, then all integers
2, 3, 4, 5, 6....11 are relatively prime to 13
To determine which positive integers less than 12 are relatively prime to 13, you need to find integers that have no common factors with 13.
Here's how you can approach it:
1. Make a list of positive integers less than 12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
2. Check if each integer has any common factors with 13. To do this, calculate the greatest common divisor (GCD) between each integer and 13.
For example, to check if 2 is relatively prime to 13, find the GCD of 2 and 13:
GCD(2, 13) = 1
If the GCD is 1, it means the integers have no common factors, and they are relatively prime to 13.
3. Go through the list of integers and find those where the GCD with 13 is 1. These integers are relatively prime to 13.
In this case, all integers from 2 to 11 are relatively prime to 13 because their GCD with 13 is 1.
Therefore, all positive integers less than 12 (2, 3, 4, 5, 6, 7, 8, 9, 10, 11) are relatively prime to 13 since 13 has no factors other than 1 and itself.