Is the number 15 a composite number? Explain why or why not.

Yes, the number **15** is a **composite number**. Here's why: ### Definition of a Composite Number A **composite number** is a positive integer greater than 1 that has **more than two distinct positive divisors**. In other words, a composite number can be divided evenly by numbers other than just 1 and itself. ### Analyzing the Number 15 Let's examine the divisors of 15: 1. **1**: Every integer is divisible by 1. 2. **3**: \(15 \div 3 = 5\) (exact division) 3. **5**: \(15 \div 5 = 3\) (exact division) 4. **15**: The number itself. So, the positive divisors of 15 are **1, 3, 5,** and **15**. ### Conclusion Since 15 has **four** positive divisors (**1, 3, 5, 15**), and notably, it can be divided evenly by numbers **other than 1 and itself** (specifically, 3 and 5), it satisfies the definition of a **composite number**. Additionally, 15 can be expressed as the product of two prime numbers: \[ 15 = 3 \times 5 \] Both **3** and **5** are prime numbers, further confirming that 15 is composite. In contrast, a **prime number** has exactly two distinct positive divisors: 1 and itself. Since 15 has more than two divisors, it is **not** a prime number. ### Summary - **15 is a composite number** because it has divisors other than 1 and itself (specifically, 3 and 5). - It can be factored into prime numbers as \(15 = 3 \times 5\).