How many factors of 108 are prime numbers ?

Options

A. 2
B. 3
C. 5
D. 6

Answer

To determine how many factors of 108 are prime numbers, we will follow these steps:

### Step 1: Prime Factorization of 108
First, we need to perform the prime factorization of the number 108.

1. Divide 108 by the smallest prime number, which is 2:
\[ 108 \div 2 = 54 \]
2. Divide 54 by 2 again:
\[ 54 \div 2 = 27 \]
3. Now, 27 is not divisible by 2, so we move to the next prime number, which is 3:
\[ 27 \div 3 = 9 \]
4. Divide 9 by 3 again:
\[ 9 \div 3 = 3 \]
5. Finally, divide 3 by 3:
\[ 3 \div 3 = 1 \]

Thus, the prime factorization of 108 is:
\[ 108 = 2^2 \times 3^3 \]

### Step 2: Identify the Prime Factors
From the prime factorization, we can identify the prime factors of 108. The prime factors are:
- 2
- 3

### Step 3: Count the Prime Factors
Now we count the distinct prime factors we found:
- The prime factors of 108 are 2 and 3.

### Conclusion
Therefore, the number of factors of 108 that are prime numbers is **2**.

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