A number that has only two factors is prime. A number that has more than two factors is composite.
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A factor that two or more numbers share is known as a common factor.
Numbers with more than one factor pair are composite numbers.
All even numbers greater than 0 have 2 as a factor.
That would be called a "common factor" of the two (or more) numbers.
As the numbers are all prime, the only factors each of them has are 1 and the number itself. Therefore the greatest, and only, common factor of two of more prime numbers is 1.