Find the sum of factor of 50.

Options

A. 92
B. 93
C. 97
D. 91

Answer

To find the sum of the factors of 50, we will follow these steps:

### Step 1: Prime Factorization of 50
First, we need to find the prime factorization of 50. We can do this by dividing 50 by the smallest prime number until we reach 1.

- 50 ÷ 2 = 25 (2 is a prime factor)
- 25 ÷ 5 = 5 (5 is a prime factor)
- 5 ÷ 5 = 1

So, the prime factorization of 50 is:
\[ 50 = 2^1 \times 5^2 \]

### Step 2: Use the Formula for the Sum of Factors
The formula for the sum of the factors of a number based on its prime factorization \( p_1^{k_1} \times p_2^{k_2} \) is given by:
\[ (1 + p_1 + p_1^2 + \ldots + p_1^{k_1})(1 + p_2 + p_2^2 + \ldots + p_2^{k_2}) \]

For our case, where \( 50 = 2^1 \times 5^2 \):
- \( p_1 = 2 \), \( k_1 = 1 \)
- \( p_2 = 5 \), \( k_2 = 2 \)

### Step 3: Calculate Each Part of the Formula
Now we will calculate each part of the formula:

1. For \( 2^1 \):
\[ 1 + 2 = 3 \]

2. For \( 5^2 \):
\[ 1 + 5 + 25 = 31 \]

### Step 4: Multiply the Results
Now we multiply the results from the two parts:
\[ 3 \times 31 = 93 \]

### Conclusion
Thus, the sum of the factors of 50 is:
\[ \text{Sum of factors} = 93 \]