GCD from Prime Decomposition/Examples/p^2 q and p q r

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Example of Use of GCD from Prime Decomposition

The greatest common divisor of $p^2 q$ and $p q r$, where $p$, $q$ and $r$ are all primes, is:

$\gcd \set {p^2 q, p q r} = p q$


\(\ds p^2 q\) \(=\) \(\ds p^2 q^1 r^0\)
\(\ds p q r\) \(=\) \(\ds p^1 q^1 r^1\)
\(\ds \leadsto \ \ \) \(\ds \gcd \set {p^2 q, p q r}\) \(=\) \(\ds p^1 q^1 r^0\)
\(\ds \) \(=\) \(\ds p q\)