jmc

We first recognize that $132=11\times 12$, so its prime factorization is $132=2^2\cdot 3\cdot 11$. We only need to see if these three prime factors will divide into $6432$. Indeed, $6432$ will satisfy the divisibility properties for both $3$ and $4$, and we can long divide to see that $11$ does not divide into $6432$. Thus, the greatest common factor is $3\times 4=12$. The greatest common factor increased by 11 is $12+11=\boxed{23}$.