Find the prime factors of the following:
`3465`

Answer

To find the prime factors of 3465, we can follow these steps:

### Step-by-Step Solution:

1. **Divide by the smallest prime number (3)**:
- Check if 3465 is divisible by 3.
- Sum of the digits: \(3 + 4 + 6 + 5 = 18\) (which is divisible by 3).
- Divide: \(3465 \div 3 = 1155\).

2. **Divide 1155 by 3 again**:
- Check if 1155 is divisible by 3.
- Sum of the digits: \(1 + 1 + 5 + 5 = 12\) (which is divisible by 3).
- Divide: \(1155 \div 3 = 385\).

3. **Divide 385 by the next smallest prime number (5)**:
- Check if 385 is divisible by 5 (it ends in 5).
- Divide: \(385 \div 5 = 77\).

4. **Divide 77 by the next smallest prime number (7)**:
- Check if 77 is divisible by 7.
- Divide: \(77 \div 7 = 11\).

5. **Divide 11 by itself (11)**:
- 11 is a prime number, and dividing it by itself gives us 1.
- Divide: \(11 \div 11 = 1\).

### Summary of Prime Factors:
The prime factors of 3465 are:
- \(3, 3, 5, 7, 11\)

Thus, the complete prime factorization of 3465 is:
\[ 3^2 \times 5^1 \times 7^1 \times 11^1 \]