co-prime
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That would be called a "common factor" of the two (or more) numbers.
All numbers have a common factor of 1. Sometimes that's the only common factor.
No. Every set of numbers has 1 as a common factor.
The greatest common factor is a number that divides evenly into two or more numbers. It is also called the highest common factor or greatest common divisor.
The greatest common factor of two or more prime numbers is 1.