The mean of the prime factors of 24 is-

Options

A. 2
B. 2.5
C. 4
D. 7.5

Answer

To find the mean of the prime factors of 24, we will follow these steps:

### Step 1: Identify the prime factors of 24
First, we need to find the prime factors of 24. The prime factorization of 24 can be done as follows:
- Start by dividing 24 by the smallest prime number, which is 2.
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 is a prime number.

So, the prime factorization of 24 is:
\[ 24 = 2^3 \times 3^1 \]

The prime factors of 24 are therefore 2 and 3.

### Step 2: List the prime factors
From the factorization, we see that the prime factors of 24 are:
- 2
- 3

### Step 3: Calculate the sum of the prime factors
Next, we need to calculate the sum of the prime factors:
\[ \text{Sum} = 2 + 3 = 5 \]

### Step 4: Count the number of prime factors
Now, we count the number of prime factors:
- There are 2 prime factors (2 and 3).

### Step 5: Calculate the mean
Finally, we calculate the mean of the prime factors using the formula:
\[ \text{Mean} = \frac{\text{Sum of prime factors}}{\text{Number of prime factors}} \]
Substituting the values we found:
\[ \text{Mean} = \frac{5}{2} = 2.5 \]

Thus, the mean of the prime factors of 24 is **2.5**.

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