No. 34 is composite and so it cannot be a prime factor.
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18 factors to [2 3 3] 34 factors to [2 17] They have a common factor of 2, so they are not coprime.
The prime factors of 34 are: 2, 17
Any power of 3 from the first upwards (31, 32, 33, 34, 35, ...).
It is a factor of 132, not a prime factor.
The factors of 34 are 1, 2, 17, 34 The prime factors are 2 and 17.