If \(p\), then is only has two divisor, 1 and \(p\). This means the greatest common divisor of \(p\) and an integer \(a\) is either \(p\) or 1. If \(p \nmid a\), then there greatest common divisor can only be 1.
$$ \gcd(p, a) = 1 $$
If \(p\), then is only has two divisor, 1 and \(p\). This means the greatest common divisor of \(p\) and an integer \(a\) is either \(p\) or 1. If \(p \nmid a\), then there greatest common divisor can only be 1.