If n is the digit at hundred place in 299156 then find out the total number of factors of 6n?

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.

This math problem explores place value and factorization. Learn how to find the total factors of 6n when n is the hundreds digit in 299156. Suitable for Grades 6-8, it covers prime factorization and counting factors.

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