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.
Question:
How many positive whole-number divisors does 196 have?
Answer:
Let's think step by step.

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9
How many positive whole-number divisors does 196 have?
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