Which of the following is an odd composite number? Options are (a) 13 (b) 17 (c) 12 (d) 15.

Options

A. 13
B. 17
C. 12
D. 15

Answer

To determine which of the given options is an odd composite number, we will analyze each option step by step.

### Step 1: Understand the definitions
- **Composite Number**: A composite number is a positive integer that has at least one positive divisor other than one or itself. In simpler terms, it has more than two factors.
- **Odd Number**: An odd number is an integer that is not divisible by 2.

### Step 2: Analyze each option

#### Option (a): 13
- Prime factorization: 13 can only be expressed as 1 × 13.
- Since it has only two factors (1 and 13), it is a **prime number**, not a composite number.

**Hint**: Check if the number has more than two factors to determine if it is composite.

#### Option (b): 17
- Prime factorization: 17 can only be expressed as 1 × 17.
- Like 13, it has only two factors (1 and 17), so it is also a **prime number**, not a composite number.

**Hint**: Remember that prime numbers cannot be composite.

#### Option (c): 12
- Prime factorization: 12 can be expressed as 2 × 2 × 3 (or 2² × 3).
- It has more than two factors: 1, 2, 3, 4, 6, and 12. Therefore, 12 is a **composite number**.
- However, 12 is an **even number**.

**Hint**: Identify whether the composite number is odd or even.

#### Option (d): 15
- Prime factorization: 15 can be expressed as 3 × 5.
- It has more than two factors: 1, 3, 5, and 15. Therefore, 15 is a **composite number**.
- Additionally, 15 is an **odd number**.

**Hint**: Check if the composite number is odd to satisfy the question's requirement.

### Conclusion
Among the options, only option (d) 15 is an odd composite number.

**Final Answer**: 15