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The GCF of 10 and 30 is 10.
Solución
The **Greatest Common Factor (GCF)** of two numbers is the largest number that divides both of them without leaving a remainder. Let's find the GCF of **10** and **30** using two different methods:
### Method 1: Listing the Factors
1. **List the factors of each number:**
- **Factors of 10:** 1, 2, 5, 10
- **Factors of 30:** 1, 2, 3, 5, 6, 10, 15, 30
2. **Identify the common factors:**
- Common factors of 10 and 30 are **1, 2, 5, 10**
3. **Determine the greatest common factor:**
- The largest number in the common factors list is **10**
### Method 2: Prime Factorization
1. **Find the prime factors of each number:**
- **10:** 2 × 5
- **30:** 2 × 3 × 5
2. **Identify the common prime factors:**
- Both numbers have the prime factors **2** and **5**
3. **Multiply the common prime factors:**
- GCF = 2 × 5 = **10**
### Conclusion
Using either method, the **Greatest Common Factor of 10 and 30 is 10**.
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The greatest common factor (GCF) of 10 and 30 is 10. To find it, you can list the factors: for 10, they're 1, 2, 5, and 10; for 30, they're 1, 2, 3, 5, 6, 10, 15, and 30. The largest factor that both numbers share is 10, making it the GCF! Did you know that the concept of GCF can be traced back to ancient civilizations, including the Greeks, who were among the first to explore the relationships between numbers? They used methods similar to what we now call the Euclidean algorithm to find common factors and deepen their understanding of division and multiplication!
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