calculate sum of factors of 60.

Answer

To calculate the sum of factors of 60, we can follow these steps:

### Step 1: Find the prime factorization of 60.
To do this, we divide 60 by the smallest prime numbers until we reach 1.

- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1

So, the prime factorization of 60 is:
\[ 60 = 2^2 \times 3^1 \times 5^1 \]

### 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 \( p_1^{k_1} \times p_2^{k_2} \times \ldots \times p_n^{k_n} \) is given by:
\[ (1 + p_1 + p_1^2 + \ldots + p_1^{k_1})(1 + p_2 + \ldots + p_2^{k_2}) \ldots (1 + p_n + \ldots + p_n^{k_n}) \]

For our case, we have:
- \( p_1 = 2, k_1 = 2 \)
- \( p_2 = 3, k_2 = 1 \)
- \( p_3 = 5, k_3 = 1 \)

### Step 3: Calculate each term.
1. For \( 2^2 \):
\[ 1 + 2 + 2^2 = 1 + 2 + 4 = 7 \]

2. For \( 3^1 \):
\[ 1 + 3 = 4 \]

3. For \( 5^1 \):
\[ 1 + 5 = 6 \]

### Step 4: Multiply the results.
Now, we multiply the sums we calculated:
\[ 7 \times 4 \times 6 \]

Calculating this step-by-step:
- First, calculate \( 7 \times 4 = 28 \)
- Then, calculate \( 28 \times 6 = 168 \)

### Step 5: Conclusion.
Thus, the sum of the factors of 60 is:
\[ \text{Sum of factors} = 168 \]