To solve this, let’s go through each step:

1. Identify the Hundreds Place Digit: In the number 299156, the hundreds place digit is 1. So, $n = 1$.

2. Calculate $6n$: $6n = 6 \times 1 = 6$

3. Find the Factors of 6:

   • The prime factorization of $6$ is: $6 = 2 \times 3$
   • Since $6 = 2^1 \times 3^1$, the formula to find the number of factors for any number with prime factorization $p_1^{a_1} \times p_2^{a_2} \times \ldots \times p_k^{a_k}$ is: $(a_1 + 1)(a_2 + 1) \ldots (a_k + 1)$
   • Here, $a_1 = 1$ and $a_2 = 1$, so the number of factors of $6$ is: $(1+1)(1+1) = 2 \times 2 = 4$

4. Conclusion: The total number of factors of $6n = 6$ is 4.

Let me know if you want more details or have any questions.

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Related Questions:

1. What are the factors of a number with a prime factorization of $p_1^2 \times p_2^3$?
2. How do you find the number of factors of a number using prime factorization?
3. If a number is a product of three distinct primes, how many factors will it have?
4. What is the total number of factors of 12?
5. How do you find the prime factorization of a composite number?

Tip:

To find the number of factors of any number, use its prime factorization and apply the formula: multiply one more than each exponent in the prime factorization.