The mean of all the factors of 12 is

Options

A. `3(2)/3`
B. `4(3)/2`
C. `4(2)/3`
D. 12

Answer

To find the mean of all the factors of 12, we will follow these steps:

### Step 1: Identify the factors of 12
The factors of a number are the integers that can be multiplied together to produce that number. For 12, the factors are:
- 1
- 2
- 3
- 4
- 6
- 12

So, the factors of 12 are: **1, 2, 3, 4, 6, 12**.

### Step 2: Calculate the sum of the factors
Now, we will add all the factors together:
\[ 1 + 2 + 3 + 4 + 6 + 12 \]
Calculating this step-by-step:
- \(1 + 2 = 3\)
- \(3 + 3 = 6\)
- \(6 + 4 = 10\)
- \(10 + 6 = 16\)
- \(16 + 12 = 28\)

So, the sum of the factors is **28**.

### Step 3: Count the number of factors
Next, we need to count how many factors there are. From our list, we see that there are **6 factors**.

### Step 4: Calculate the mean
The mean is calculated by dividing the sum of the factors by the number of factors. Therefore, we have:
\[ \text{Mean} = \frac{\text{Sum of factors}}{\text{Number of factors}} = \frac{28}{6} \]
Now, we can simplify \( \frac{28}{6} \):
- Dividing both the numerator and the denominator by 2 gives us:
\[ \frac{28 \div 2}{6 \div 2} = \frac{14}{3} \]

### Step 5: Convert to a mixed fraction (if needed)
To convert \( \frac{14}{3} \) into a mixed fraction:
- \(14\) divided by \(3\) gives \(4\) with a remainder of \(2\).
- So, \( \frac{14}{3} = 4 \frac{2}{3} \).

Thus, the mean of all the factors of 12 is **\(4 \frac{2}{3}\)**.

### Final Answer
The mean of all the factors of 12 is **\(4 \frac{2}{3}\)**.

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