No, 1 is not a Prime number.
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15 and 37 are co-prime because they have no common factor greater than 1.
1, 3, 5 are all prime factors of 15 3 and 5 only. 1 is a special number that has no factors but itself yet it is not counted as a prime number.
15 is a factor of 45, but it is not a prime number.
Because 7 is prime, the highest, lowest and only common factor of 15 and 7 is 1 (one).
Numbers called relatively prime have no common factors other than 1. All even numbers have 2 as a common factor, so no even number is relatively prime with any other even number. As an example, the factors of 14 are 1, 2, 7, and 14, and the factors of 15 are 1, 3, 5, and 15. 14 and 15 are relatively prime because the only factor they have in common is 1.