TITLE: Difference between | and /
QUESTION [5 upvotes]: "If we find a prime $p$ such that $p\mid n$ , then $n/p$ is a positive integer that's smaller than $n$." 
I understand $n/p$ is $n$ divided by $p$ but what is $n\mid p$?

REPLY [5 votes]: The expression "$n/p$" represents the number that you get when you divide $n$ by $p$, whereas the expression "$p\mid n$" represents the statement that $p$ divides evenly into $n$.