Okay, so I need to figure out how many positive whole-number divisors 196 has. Hmm, let me start by recalling that a divisor of a number is another number that can divide it without leaving a remainder. So, for example, 1 and the number itself are always divisors. But 196 is a specific number, so maybe I can break it down into its prime factors first? That usually helps with problems like this.

Let me try factoring 196. I know that 196 is an even number because it ends with a 6, so it's divisible by 2. Let me divide it by 2: 196 ÷ 2 = 98. Okay, 98 is still even, so divide by 2 again: 98 ÷ 2 = 49. Now, 49 is a number I recognize. That's 7 squared, right? So 49 ÷ 7 = 7, and then 7 ÷ 7 = 1. So putting that all together, the prime factors of 196 are 2 × 2 × 7 × 7. Wait, that can be written as 2² × 7². 

Once I have the prime factorization, there's a formula to find the number of divisors. I remember it's something like taking the exponents of the prime factors, adding one to each, and then multiplying them together. So in this case, the exponents are 2 and 2 for primes 2 and 7 respectively. Adding one to each gives 3 and 3. Multiplying 3 × 3 = 9. So does that mean 196 has 9 divisors? Let me check by listing them out to make sure I didn't make a mistake.

Starting from 1: 1 is a divisor. Then 2, since it's even. 4, because 2² is a factor. Then 7, since 7 is a prime factor. 14 (2×7), 28 (4×7), 49 (7²), 98 (14×7), and 196 itself. Let me count those: 1, 2, 4, 7, 14, 28, 49, 98, 196. That's nine numbers. Yep, that matches the formula's result. So the answer should be 9. 

Wait, just to be thorough, let me think again. The prime factorization was 2² × 7². The formula for the number of divisors is indeed (exponent of 2 + 1) × (exponent of 7 + 1) = (2+1)(2+1) = 3×3 =9. That seems right. And when I listed them out, I got exactly nine divisors. So I think that's correct. 

I don't see any mistakes in my reasoning here. The key steps were factoring 196 into primes, applying the formula, and verifying by listing all possible divisors. All checks out. So the answer should be 9.
Therefore, the number of positive whole-number divisors that 196 has is $\boxed{9}$.
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