Write the following sets in roster form and also in set builder form :
the set of factors of 24

Answer

To solve the problem of writing the set of factors of 24 in both roster form and set builder form, we will follow these steps:

### Step 1: Identify the factors of 24
Factors of a number are the integers that can be multiplied together to produce that number. We need to find all the integers that divide 24 without leaving a remainder.

### Step 2: List the factors of 24
The factors of 24 are:
1. 1 (1 x 24)
2. 2 (2 x 12)
3. 3 (3 x 8)
4. 4 (4 x 6)
5. 6 (6 x 4)
6. 8 (8 x 3)
7. 12 (12 x 2)
8. 24 (24 x 1)

So, the complete list of factors of 24 is: 1, 2, 3, 4, 6, 8, 12, 24.

### Step 3: Write the factors in roster form
Roster form lists all the elements of a set explicitly. Therefore, the set of factors of 24 in roster form is:
\[ A = \{ 1, 2, 3, 4, 6, 8, 12, 24 \} \]

### Step 4: Write the factors in set builder form
Set builder form describes the properties that characterize the elements of the set. For the factors of 24, we can express it as:
\[ A = \{ x \mid x \text{ is a factor of } 24 \} \]

### Final Answer
- Roster Form: \( A = \{ 1, 2, 3, 4, 6, 8, 12, 24 \} \)
- Set Builder Form: \( A = \{ x \mid x \text{ is a factor of } 24 \} \)