Find the sum of factors of 50? A] 97 B] 91 C] 80 D] 93 Options : A B C D

Step 1: Break Down the Problem

To find the sum of the factors of a number, we first need to identify its factors.

Step 2: Relevant Concepts

Factors of a number are the integers that divide that number without leaving a remainder. For any integer $n$, if $p_1^{k_1} \times p_2^{k_2} \times \ldots \times p_m^{k_m}$ is the prime factorization, the sum of the factors can be calculated using the formula:

$\sigma(n) = (1 + p_1 + p_1^2 + \ldots + p_1^{k_1})(1 + p_2 + p_2^2 + \ldots + p_2^{k_2}) \ldots (1 + p_m + p_m^2 + \ldots + p_m^{k_m})$

Step 3: Analysis and Detail

1. Find the prime factorization of 50: $50 = 2^1 \times 5^2$

2. Apply the formula for the sum of factors:

   • For $2^1$: $1 + 2 = 3$
   • For $5^2$: $1 + 5 + 25 = 31$

3. Multiply the results: $\sigma(50) = 3 \times 31 = 93$

Step 4: Verify and Summarize

The factors of 50 are: 1, 2, 5, 10, 25, and 50. Their sum is: $1 + 2 + 5 + 10 + 25 + 50 = 93$ Thus, the calculations are verified.

Final Answer

The sum of the factors of 50 is 93. Thus, the correct option is D.