Calculating p-adic valuation $v_p(n)$, using basic properties

Question

Calculating p-adic valuation $v_p(n)$ I'm not confident with the properties of $v_p(n)$ Where $v_p(n) = $ the biggest integer $e$ such that $p^e$ divides $n$, if $n\not=0$, and $+\infty$ if $n=0$.

Would I be correct in calculating $v_3(50!/{25!25!})$ By calculating $v_3(50!)-v_3(25!)-v_3(25!)$ ?

Answer 1

$v_p(n) = $ the biggest integer $e$ such that $p^e$ divides $n$, if $n\not=0$, and $+\infty$ if $n=0$. For the rest you are right, as the function $v_p$ as defined "by me" is multiplicative : $v_p(nn') = v_p(n) v_p(n')$ for $n,n'$ non zero integers.