Let P = { x: x is a factor of 18 } and Q = { x : x is a factor of 24}.
Write each one of P and Q in Roster form.

Answer

To write the sets P and Q in roster form, we need to identify the factors of 18 and 24.

### Step 1: Identify the factors of 18
- The factors of a number are the integers that can be multiplied together to get that number.
- For 18, we can find the factors by checking which numbers divide 18 without leaving a remainder.

**Factors of 18:**
1. 1 (1 × 18 = 18)
2. 2 (2 × 9 = 18)
3. 3 (3 × 6 = 18)
4. 6 (6 × 3 = 18)
5. 9 (9 × 2 = 18)
6. 18 (18 × 1 = 18)

Thus, the factors of 18 are: **1, 2, 3, 6, 9, 18**.

### Step 2: Write set P in roster form
- Set P is defined as the set of all factors of 18.

**Set P in roster form:**
P = {1, 2, 3, 6, 9, 18}

### Step 3: Identify the factors of 24
- Similarly, we will find the factors of 24.

**Factors of 24:**
1. 1 (1 × 24 = 24)
2. 2 (2 × 12 = 24)
3. 3 (3 × 8 = 24)
4. 4 (4 × 6 = 24)
5. 6 (6 × 4 = 24)
6. 8 (8 × 3 = 24)
7. 12 (12 × 2 = 24)
8. 24 (24 × 1 = 24)

Thus, the factors of 24 are: **1, 2, 3, 4, 6, 8, 12, 24**.

### Step 4: Write set Q in roster form
- Set Q is defined as the set of all factors of 24.

**Set Q in roster form:**
Q = {1, 2, 3, 4, 6, 8, 12, 24}

### Final Answer:
- Set P = {1, 2, 3, 6, 9, 18}
- Set Q = {1, 2, 3, 4, 6, 8, 12, 24}

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