Find the sum of factors of 2240.

Correct option is C

Given:

The number to find the sum of factors is 2240.

Formula Used:

The sum of factors of a number n can be calculated using its prime factorization:

​$$n = p_1^{e_1} \cdot p_2^{e_2} \cdot \ldots \cdot p_k^{e_k}$$​​

The sum of factors is given by:

​$$\text{Sum of factors} = (1 + p_1 + p_1^2 + \ldots + p_1^{e_1}) \cdot (1 + p_2 + p_2^2 + \ldots + p_2^{e_2}) \cdot \ldots$$​​

Solution:

1. Perform prime factorization of 2240:

​$$2240 = 2^6 \cdot 5^1 \cdot 7^1$$​​

2. Use the formula for the sum of factors:

​$$(1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6) \cdot (1 + 5) \cdot (1 + 7)$$​​

3. Calculate each term:

​$$1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127$$​​

1 + 5 = 6

1 + 7 = 8

4. Multiply the results:

​$$\text{Sum of factors} = 127 \cdot 6 \cdot 8 = 6096$$​​

Final Answer:

(C) 6096