The numbers 38 and 40 are not relatively prime because they share a common factor greater than 1. To determine if two numbers are relatively prime, we need to find their greatest common divisor (GCD).
First, let's factor both numbers:
- The prime factorization of 38 is \(2 \times 19\).
- The prime factorization of 40 is \(2^3 \times 5\).
The only common factor between the two numbers is 2. Since 2 is greater than 1, 38 and 40 are not relatively prime. Two numbers are considered relatively prime if their GCD is 1, which is not the case for 38 and 40.
Therefore, Stephen is incorrect in stating that 38 and 40 are relatively prime.
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