solution: 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 $12+11 = \boxed{23}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  What is the result when the greatest common factor of 6432 and 132 is increased by 11?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 23
extra_info.question: What is the result when the greatest common factor of 6432 and 132 is increased by 11?
extra_info.split: test