Yes. Since 127 is a Prime number it is also a prime factor.
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This is tricky. Once you determine that 73 is a prime number then you can ignore 127 (since 73 is not a factor of 127). So, the greatest common factor is 1. Note: if you asked 73 and 146 then the answer would be 73. Anytime one of the numbers is a prime - then the answer is EITHER 1 or the prime number (if the other number is a multiple of the prime).
129 3,43
35 can be a factor, but it is not prime.
There is no factorization. 37 is a prime number.37 is already prime. Its only prime factor is itself.
81 is not prime. Its prime factorization is 3x3x3x3.