How many factors of 45 are prime numbers?

Options

A. 3
B. 4
C. 5
D. 2

Answer

To determine how many factors of 45 are prime numbers, we can follow these steps:

### Step 1: Find the prime factorization of 45
To find the prime factorization, we start dividing 45 by the smallest prime numbers.

- **Divide by 2**: 45 is odd, so it is not divisible by 2.
- **Divide by 3**:
\[ 45 \div 3 = 15 \]
- **Divide 15 by 3**:
\[ 15 \div 3 = 5 \]
- **Divide 5 by 5**:
\[ 5 \div 5 = 1 \]

Thus, the prime factorization of 45 is:
\[ 45 = 3^2 \times 5^1 \]

### Step 2: Identify the prime factors
From the prime factorization \(3^2 \times 5^1\), we can see that the prime factors of 45 are:
- 3
- 5

### Step 3: Count the prime factors
Now we count the distinct prime factors:
- The prime factors we found are 3 and 5.

### Conclusion
Thus, the number of factors of 45 that are prime numbers is **2**.