How many positive factors of 74 are there?

Options

A. 5
B. 6
C. 4
D. 3

Answer

To find how many positive factors of 74 there are, we can follow these steps:

### Step 1: Prime Factorization of 74
First, we need to perform the prime factorization of 74. We can divide 74 by the smallest prime number, which is 2.

\[ 74 \div 2 = 37 \]

Since 37 is a prime number, we can write the prime factorization of 74 as:

\[ 74 = 2^1 \times 37^1 \]

### Step 2: Using the Formula for Counting Factors
To find the number of positive factors of a number based on its prime factorization, we can use the formula:

\[ \text{Number of factors} = (p_1 + 1)(p_2 + 1)(p_3 + 1) \ldots \]

where \( p_1, p_2, p_3, \ldots \) are the powers of the prime factors.

In our case, we have:

- For the prime factor \( 2^1 \), \( p_1 = 1 \)
- For the prime factor \( 37^1 \), \( p_2 = 1 \)

Now we can apply the formula:

\[ \text{Number of factors} = (1 + 1)(1 + 1) = 2 \times 2 = 4 \]

### Step 3: Conclusion
Thus, the number of positive factors of 74 is 4.

### Final Answer
The correct answer is **4**.

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