There are infinitely many such pairs.
For example,
suppose p, q, r and s are 4 prime numbers.
Then p*q and r*s are both composite but p*q and r*s are coprime.
And you could always mutiply either one of them by the prime number t, and maybe the other one by another r to give p*q*t and r2*s. And so on.
So, for example 2*7 = 14
and 3*5 = 15 form such a pair.
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Two composite numbers may or may not be relatively prime, depending on their factors. Relatively prime numbers are sets of two or more numbers having 1 as their greatest common factor (gcf). All even numbers have 2 as a common factor, so no even number is relatively prime with any other even number.
A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite. 45 and 102 are both composite.
The sum of two prime numbers will be composite unless one of the prime numbers is 2.
All the even numbers greater than 2 are composite.
112 is composite. Its prime factorization is 2*2*2*2*7. All even numbers are composite except for 2.