The sum of factors of 1520 except the unity is :

Options

A. 3720
B. 2730
C. 2370
D. None of these

Answer

To find the sum of the factors of 1520 except for unity (1), we can follow these steps:

### Step 1: Find the prime factorization of 1520.
To find the prime factors, we divide 1520 by the smallest prime numbers until we reach 1.

- 1520 ÷ 2 = 760
- 760 ÷ 2 = 380
- 380 ÷ 2 = 190
- 190 ÷ 2 = 95
- 95 ÷ 5 = 19
- 19 ÷ 19 = 1

So, the prime factorization of 1520 is:
\[ 1520 = 2^4 \times 5^1 \times 19^1 \]

### Step 2: Find all the factors of 1520.
To find the factors, we can use the prime factorization. The factors can be generated by taking all combinations of the prime factors:

The exponents of the prime factors are:
- For \(2\): 0 to 4 (5 options)
- For \(5\): 0 to 1 (2 options)
- For \(19\): 0 to 1 (2 options)

The total number of factors is given by multiplying the number of options:
\[ (4+1)(1+1)(1+1) = 5 \times 2 \times 2 = 20 \]

### Step 3: List the factors of 1520.
The factors of 1520 are:
1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 95, 152, 190, 304, 380, 760, 1520

### Step 4: Exclude unity (1) from the list of factors.
Now we will exclude 1 from the list:
2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 95, 152, 190, 304, 380, 760, 1520

### Step 5: Calculate the sum of the remaining factors.
Now we will add all the factors except for 1:
\[ 2 + 4 + 5 + 8 + 10 + 16 + 19 + 20 + 38 + 40 + 76 + 95 + 152 + 190 + 304 + 380 + 760 + 1520 \]

Calculating this step by step:
- \(2 + 4 = 6\)
- \(6 + 5 = 11\)
- \(11 + 8 = 19\)
- \(19 + 10 = 29\)
- \(29 + 16 = 45\)
- \(45 + 19 = 64\)
- \(64 + 20 = 84\)
- \(84 + 38 = 122\)
- \(122 + 40 = 162\)
- \(162 + 76 = 238\)
- \(238 + 95 = 333\)
- \(333 + 152 = 485\)
- \(485 + 190 = 675\)
- \(675 + 304 = 979\)
- \(979 + 380 = 1359\)
- \(1359 + 760 = 2119\)
- \(2119 + 1520 = 3639\)

### Final Answer:
The sum of the factors of 1520 except for unity is **3639**.

---