Final answer:
Positive integers less than 50 that are relatively prime to 50 are those not divisible by 2 or 5. The list includes 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, and 49.
Step-by-step explanation:
To find all positive integers that are relatively prime to 50, we must identify the numbers less than 50 that do not share any factors with 50 aside from 1. The number 50 is factored into 2 × 5 × 5. Therefore, any positive integer that does not include the prime factors 2 or 5 is relatively prime to 50.
Numbers that are multiples of 2 or 5 are automatically excluded. Here is the complete list of positive integers less than 50 that are relatively prime to 50: 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49. These numbers comprise all the positive integers up to 50 that are not divisible by either 2 or 5.