No.
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No, they are not.
yes
No, they are not.
The factors of 35 are 1, 5, 7, and 35. The factors of 27 are 1, 3, 9, and 27. The only factor they have in common is 1; therefore, 35 and 27 are relatively prime. Alternatively, you can look at the prime factors. The prime factors of 35 are 5 and 7. The prime factors of 27 are 3, 3, and 3. They have no prime factors in common, so they are relatively prime, which means their only common factor is 1.
35 and 49, among others.