No, coprime numbers have no common factors other than one; 15 and 24 both have the factor 3, so they are not coprime.
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As 13 is prime and is not a factor of 24, then they are relatively prime
13 and 24 are relatively prime.
No, they are not relatively prime.
16 and 24 are not relatively prime. They have 2 as a common factor.
Yes, they are relatively prime.