Find the difference between the median and mean of factors of 42.

Answer

To find the difference between the median and mean of the factors of 42, we will follow these steps:

### Step 1: Find the factors of 42.
The factors of 42 are the numbers that divide 42 without leaving a remainder. We can find them by checking the numbers from 1 to 42.

- 1 (42 ÷ 1 = 42)
- 2 (42 ÷ 2 = 21)
- 3 (42 ÷ 3 = 14)
- 6 (42 ÷ 6 = 7)
- 7 (42 ÷ 7 = 6)
- 14 (42 ÷ 14 = 3)
- 21 (42 ÷ 21 = 2)
- 42 (42 ÷ 42 = 1)

Thus, the factors of 42 are: **1, 2, 3, 6, 7, 14, 21, 42**.

### Step 2: Count the number of factors.
We have the factors: 1, 2, 3, 6, 7, 14, 21, 42.
The total number of factors is **8**.

### Step 3: Find the median.
Since there are 8 factors (an even number), the median will be the average of the two middle numbers in the sorted list of factors.

The sorted list of factors is: **1, 2, 3, 6, 7, 14, 21, 42**.

The two middle numbers (4th and 5th) are 6 and 7.

Median = (6 + 7) / 2 = 13 / 2 = **6.5**.

### Step 4: Find the mean.
The mean is calculated by taking the sum of all the factors and dividing it by the number of factors.

Sum of factors = 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 = **96**.

Mean = Sum of factors / Number of factors = 96 / 8 = **12**.

### Step 5: Find the difference between the mean and median.
Difference = Mean - Median = 12 - 6.5 = **5.5**.

### Final Answer:
The difference between the median and mean of the factors of 42 is **5.5**.

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