Find the number of factors of `1498176` and also their sum.

Answer

To find the number of factors of `1498176` and their sum, we will follow these steps:

### Step 1: Prime Factorization
We need to factor `1498176` into its prime factors.

1. Start dividing by the smallest prime number, which is `2`.
- \( 1498176 \div 2 = 749088 \)
- \( 749088 \div 2 = 374544 \)
- \( 374544 \div 2 = 187272 \)
- \( 187272 \div 2 = 93636 \)
- \( 93636 \div 2 = 46818 \)
- \( 46818 \div 2 = 23409 \) (now we cannot divide by 2 anymore since 23409 is odd)

2. Next, divide by `3`.
- \( 23409 \div 3 = 7803 \)
- \( 7803 \div 3 = 2601 \)
- \( 2601 \div 3 = 867 \)
- \( 867 \div 3 = 289 \) (now we cannot divide by 3 anymore)

3. Now, we factor `289` which is \( 17 \times 17 \) or \( 17^2 \).

Putting this all together, we have:
\[ 1498176 = 2^6 \times 3^4 \times 17^2 \]

### Step 2: Number of Factors
To find the number of factors, we use the formula:
\[ \text{Number of factors} = (a + 1)(b + 1)(c + 1) \]
where \( a, b, c \) are the powers of the prime factors.

From our factorization:
- \( a = 6 \) (for \( 2^6 \))
- \( b = 4 \) (for \( 3^4 \))
- \( c = 2 \) (for \( 17^2 \))

Now substituting these values:
\[ \text{Number of factors} = (6 + 1)(4 + 1)(2 + 1) = 7 \times 5 \times 3 = 105 \]

### Step 3: Sum of Factors
To find the sum of the factors, we use the formula:
\[ \text{Sum of factors} = \left(\frac{p_1^{k_1 + 1} - 1}{p_1 - 1}\right) \times \left(\frac{p_2^{k_2 + 1} - 1}{p_2 - 1}\right) \times \left(\frac{p_3^{k_3 + 1} - 1}{p_3 - 1}\right) \]
where \( p_1, p_2, p_3 \) are the prime factors and \( k_1, k_2, k_3 \) are their respective powers.

Substituting the values:
- For \( 2^6 \):
\[ \frac{2^{6 + 1} - 1}{2 - 1} = \frac{2^7 - 1}{1} = 127 \]

- For \( 3^4 \):
\[ \frac{3^{4 + 1} - 1}{3 - 1} = \frac{3^5 - 1}{2} = \frac{243 - 1}{2} = \frac{242}{2} = 121 \]

- For \( 17^2 \):
\[ \frac{17^{2 + 1} - 1}{17 - 1} = \frac{17^3 - 1}{16} = \frac{4913 - 1}{16} = \frac{4912}{16} = 307 \]

Now, multiplying these sums together:
\[ \text{Sum of factors} = 127 \times 121 \times 307 \]

Calculating this step by step:
1. \( 127 \times 121 = 15367 \)
2. \( 15367 \times 307 = 4717929 \)

### Final Answers
- The number of factors of `1498176` is **105**.
- The sum of the factors of `1498176` is **4717929**.