En primer lugar, factorizamos los números
 
$99 = 3^{2}\cdot11$
$999 = 3^{3}\cdot37$
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Buscamos los factores comunes a todos los números: 3 ,
y los elevamos a los menores exponentes
$M.C.D. ( 99 , 999 ) = 3^{2}$

$\left. \begin{array}{c|c}99 & 3\cr33 & 3 \cr11 & 11 \cr1\end{array} \right. \quad$$\left. \begin{array}{c|c}999 & 3\cr333 & 3 \cr111 & 3 \cr37 & 37 \cr1\end{array} \right. \quad$