Two numbers $a$ and $b$ are coprime if and only if $(a, b) = 1$.
$(4, 5) = 1$, are $4$ and $5$ coprime?
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$\begingroup$Two numbers $a$ and $b$ are coprime if ad only if they have no common factor or more generally H.C.F.$(a,b)=1$.
There are many numbers which do not have a common factor between them and they still are coprime. For example $(4,9)$, $(9,25)$ are coprime even when none of the numbers is prime.
In you example too, $4$ is not prime but still the pair $(4,5)$ is of coprime numbers.
$\endgroup$ $\begingroup$Two numbers $a,b$ are coprime $\iff \gcd(a,b)=1$
Thus $\gcd(4,5)=1=\gcd(2^2,5)=1$ As you see 4 doesn't share a prime factor with 5, so they are coprime. Extending this, we know that $a$ and $b$ are coprimes if they don't have prime factors in common.
$\endgroup$ $\begingroup$Yes, according to the defnition of coprime even though $4$ is not a prime number.
The only common factor between the two numbers is $1$.
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