Find the number of ordered pairs $(m,n)$ of integers that satisfy \[mn = 2m + 4n.\]
%20number%20of%20ordered%20pairs%20%24%28m%2Cn%29%24%20of%20integers%20that%20satisfy%20%5C%5Bmn%20%3D%202m%20%2B%204n.%5C%5D" id="TexFormula1" title="Find the number of ordered pairs $(m,n)$ of integers that satisfy \[mn = 2m + 4n.\]" alt="Find the number of ordered pairs $(m,n)$ of integers that satisfy \[mn = 2m + 4n.\]" align="absmiddle" class="latex-formula">
