How many positive factors of 325 are there?

Options

A. 6
B. 8
C. 12
D. 9

Answer

To find the number of positive factors of 325, we will follow these steps:

### Step 1: Prime Factorization of 325
First, we need to perform the prime factorization of 325.

- Start by dividing 325 by the smallest prime number, which is 5:
\[ 325 \div 5 = 65 \]
- Next, we factor 65. Again, we divide by 5:
\[ 65 \div 5 = 13 \]
- Now, we have 13, which is a prime number.

Thus, the prime factorization of 325 is:
\[ 325 = 5^2 \times 13^1 \]

### Step 2: Use the Formula for Counting Factors
To find the number of positive factors, we use the formula:
\[ \text{Number of positive factors} = (P + 1)(Q + 1) \]
where \( P \) and \( Q \) are the powers of the prime factors.

From our prime factorization:
- The power of 5 (P) is 2.
- The power of 13 (Q) is 1.

Now, we apply the formula:
\[ \text{Number of positive factors} = (2 + 1)(1 + 1) \]

### Step 3: Calculate the Number of Factors
Now we calculate:
\[ (2 + 1) = 3 \]
\[ (1 + 1) = 2 \]
So,
\[ \text{Number of positive factors} = 3 \times 2 = 6 \]

### Conclusion
Therefore, the number of positive factors of 325 is **6**.

---