solution: First prime factorize $196=2^2\cdot7^2$.  The prime factorization of any divisor of 196 cannot include any primes other than 2 and 7.  We are free to choose either 0, 1, or 2 as the exponent of 2 in the prime factorization of a divisor of 196.  Similarly, we may choose 0, 1, or 2 as the exponent of 7.  In total, there are $3\times 3=9$ possibilities for the prime factorization of a divisor of 196.  Distinct prime factorizations correspond to distinct integers, so there are $\boxed{9}$ divisors of 196.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  How many positive whole-number divisors does 196 have?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 9
extra_info.question: How many positive whole-number divisors does 196 have?
extra_info.split: test