Pregunta
What is the Greatest Common Factor of 35 and \( 49 \approx \)
Ask by Joseph Fernandez. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The Greatest Common Factor (GCF) of 35 and 49 is 7.
Solución
To find the **Greatest Common Factor (GCF)** of 35 and 49, you can use either the **listing factors method** or the **prime factorization method**. Here's how both methods work:
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### **1. Listing Factors Method**
**Step 1:** List all the factors of each number.
- **Factors of 35:** 1, 5, 7, 35
- **Factors of 49:** 1, 7, 49
**Step 2:** Identify the common factors.
- **Common Factors:** 1 and 7
**Step 3:** Determine the greatest of the common factors.
- **GCF:** 7
---
### **2. Prime Factorization Method**
**Step 1:** Find the prime factors of each number.
- **35:**
35 = 5 × 7
- **49:**
49 = 7 × 7
**Step 2:** Identify the common prime factors.
- Both numbers share the prime factor **7**.
**Step 3:** Multiply the common prime factors to find the GCF.
- **GCF:** 7
---
**Conclusion:**
The **Greatest Common Factor (GCF) of 35 and 49 is 7**.
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Simplifique esta solución Extra Insights
The Greatest Common Factor (GCF) of 35 and 49 is 7! This is because both numbers can be divided by 7, which is their largest shared factor. To find the GCF, you can also list out the factors: for 35, the factors are 1, 5, 7, and 35, while for 49, the factors are 1, 7, 49. The highest common factor here is indeed 7. For a quick tip, remember to use the prime factorization method! Break down each number into its prime factors: 35 = 5 x 7 and 49 = 7 x 7. Then, multiply the lowest powers of all common primes, and voila, you have your GCF! Just watch out for skipping factors - sometimes the answer can be hiding in plain sight!
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