Two numbers are co-prime when they share no common factors other than 1.
We call numbers that share no common factors “co-prime”. One does not count in the list of common factors here. Fractions are irreducible only when the top and bottom integers are co-prime.
Relationship to Regular Primes
Any prime number is co-prime with any other prime number, obviously. But any prime number is also co-prime with any number that is not evenly divisible by it.
Numbers can be co-primes even if neither number is prime. 14 & 15 are co-prime because 14 has 1, 2, 7, and 14, which shares no factors (aside from 1) with 15’s 1, 3, 5 and 15. This is why 14/15ths is an irreducible fraction.