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

1. Break Down the Problem

To find the sum of the factors of 50, we first need to determine its prime factorization. Once we have the factorization, we can use the formula for the sum of the factors.

2. Relevant Concepts

The prime factorization of 50 is: $50 = 2^1 \times 5^2$

The formula for the sum of the factors is given by: $\sigma(n) = (p_1^{k_1 + 1} - 1)/(p_1 - 1) \times (p_2^{k_2 + 1} - 1)/(p_2 - 1) \ldots$ where $p_i$ are the prime factors and $k_i$ are their respective powers.

3. Analysis and Detail

For our case:

• $p_1 = 2$, $k_1 = 1$
• $p_2 = 5$, $k_2 = 2$

Now, we apply the formula: $\sigma(50) = \left(\frac{2^{1 + 1} - 1}{2 - 1}\right) \times \left(\frac{5^{2 + 1} - 1}{5 - 1}\right)$

Calculating each part:

1. For $p_1 = 2$: $\frac{2^{2} - 1}{1} = \frac{4 - 1}{1} = 3$

2. For $p_2 = 5$: $\frac{5^{3} - 1}{4} = \frac{125 - 1}{4} = \frac{124}{4} = 31$

Combining these results: $\sigma(50) = 3 \times 31 = 93$

4. Verify and Summarize

The calculations have been verified, and the sum of the factors of 50 is indeed $93$.

Final Answer

The sum of the factors of 50 is $\boxed{93}$ (Option D).