It appears you've uploaded an image with some mathematical problems. I'll extract and solve the problems from the image for you. Let's start by identifying and analyzing each question.

Question 1: The image shows a question about the number of factors for the number 120.

To solve this:

1. Factorize 120 into its prime factors: $120 = 2^3 \times 3 \times 5$.
2. Use the formula to find the number of factors: $(e_1 + 1)(e_2 + 1)(e_3 + 1)$, where $e_1, e_2, e_3$ are the exponents of the prime factors.
   • $(3 + 1)(1 + 1)(1 + 1) = 4 \times 2 \times 2 = 16$.

So, the number of factors of 120 is 16.

Question 2: This question is about the least common multiple (LCM) of the numbers 8, 12, and 30.

To solve this:

1. Factorize each number:
   • $8 = 2^3$
   • $12 = 2^2 \times 3$
   • $30 = 2 \times 3 \times 5$
2. Take the highest power of each prime factor:
   • $2^3 \times 3 \times 5 = 120$.

The LCM of 8, 12, and 30 is 120.

Question 3: This question asks for the sum of angles in a polygon with $n$ sides (polygon internal angles).

The formula for the sum of internal angles of a polygon is: $\text{Sum of angles} = (n - 2) \times 180^\circ$

Without specific information, the sum depends on the number of sides.

Question 4: The question is about the median value of the data provided.

Without the actual data listed in the question, the answer cannot be determined directly. The median is the middle value when data is ordered from smallest to largest.

Question 5: The question involves identifying an odd characteristic number related to the given data.

Again, specific data or further details are needed to answer accurately.

Would you like any further details on these solutions? Here are some questions that extend this topic:

1. How would you find the prime factorization of a larger number, like 360?
2. What is the relationship between the LCM and the Greatest Common Divisor (GCD)?
3. Can you calculate the sum of the internal angles of a decagon (10-sided polygon)?
4. How is the mode different from the median, and in which scenarios is each more informative?
5. How would the presence of outliers affect the calculation of the median?

Tip: When calculating the LCM or GCD of several numbers, it is often helpful to first find the prime factorization of each number.