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Answer
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130.
Solution
Sure! Let's look at both the **prime factorization** of 130 and all of its **factors**.
### Prime Factorization of 130
To find the prime factors of 130:
1. **Divide by 2** (the smallest prime number):
- 130 ÷ 2 = 65 → so, 2 is a prime factor.
2. **Factor 65**:
- 65 ÷ 5 = 13 → so, 5 is a prime factor.
3. **Factor 13**:
- 13 is a prime number itself.
**Prime factors of 130:**
\[ 130 = 2 \times 5 \times 13 \]
### All Positive Factors of 130
To find all positive factors of 130, consider the combinations of its prime factors:
1. **Start with 1 and the number itself:**
- 1 and 130.
2. **Include the prime factors:**
- 2, 5, and 13.
3. **Combine the prime factors to find additional factors:**
- \(2 \times 5 = 10\)
- \(2 \times 13 = 26\)
- \(5 \times 13 = 65\)
**All positive factors of 130 are:**
\[ 1, \, 2, \, 5, \, 10, \, 13, \, 26, \, 65, \, 130 \]
If you need any more information or further assistance, feel free to ask!
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Simplify this solution Beyond the Answer
Did you know that 130 is a composite number? It’s made up of a few integral parts, specifically the factors 1, 2, 5, 10, 13, 26, 65, and 130 itself. In fact, its prime factorization is 2 × 5 × 13, making it a lovely blend of various numbers that work together! When it comes to real-world applications, understanding factors is super handy, especially in fields like finance or construction. For instance, if you were building a fence around a yard that’s exactly 130 feet long, knowing the factors can help you decide how many posts you'll need—whether you want to space them every 2 feet or every 5 feet, the factors dictate how efficiently you can use your materials!
