Yes, e.g. 3 and 5 are relatively prime, 27 (33) and 25 (52) are relatively prime...
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Any two prime numbers will be relatively prime. Numbers are relatively prime if they do not have any prime factors in common. Prime numbers have only themselves as prime factors, so all prime numbers are relatively prime to the others.
Two numbers are relatively prime if their GCF is 1.
All of the prime numbers are odd except for two.
Yes. In general, if you have two different prime numbers, they will also be relatively prime.
No. Two even numbers cannot be relatively prime.