Find the number of factors of factors of the following :
1339

Answer

To find the number of factors of the number 1339, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factors of 1339.

1339 can be expressed as:
\[ 1339 = 13 \times 103 \]

### Step 2: Express in the Form of Prime Factors
Next, we express the prime factorization in the form \( a^p \times b^q \), where \( a \) and \( b \) are the prime factors, and \( p \) and \( q \) are their respective powers.

From our factorization:
- \( a = 13 \) with \( p = 1 \)
- \( b = 103 \) with \( q = 1 \)

### Step 3: Calculate the Total Number of Factors
To find the total number of factors \( n \) of a number, we use the formula:
\[ n = (p + 1)(q + 1) \]

Substituting the values we have:
- \( p = 1 \) and \( q = 1 \)

Now, we calculate:
\[ n = (1 + 1)(1 + 1) \]
\[ n = 2 \times 2 = 4 \]

### Step 4: Conclusion
Thus, the total number of factors of 1339 is 4.

### Step 5: Factors of Factors
Now, we need to find the number of factors of the total number of factors we just calculated, which is 4.

### Step 6: Prime Factorization of 4
The prime factorization of 4 is:
\[ 4 = 2^2 \]

### Step 7: Calculate the Total Number of Factors of 4
Using the same formula for the total number of factors:
\[ n = (2 + 1) \]
\[ n = 3 \]

### Final Answer
Therefore, the number of factors of the number of factors of 1339 is **3**.

---