No.
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55 and 72 are relatively prime because they have no prime factors in common.
18 = 2 x 32 and 55 = 5 x 11 so yes it is.
Yes, 11 and 51 are relatively prime.
11 is a prime number. For it to be relatively prime, it needs to be compared to another integer.
11 and 110 are not relatively prime because they have 11 as a common factor.