Find the greatest common factor for the group of numbers. $$ 28,12,24 $$

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To find the greatest common factor (GCF) of the numbers **28**, **12**, and **24**, you can use either the **prime factorization** method or the **Euclidean algorithm**. Here's how to do it using both methods:

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### **Method 1: Prime Factorization**

1. **Factor each number into its prime factors:**
   - **28** = 2² × 7
   - **12** = 2² × 3
   - **24** = 2³ × 3

2. **Identify the common prime factors:**
   - The only common prime factor among all three numbers is **2**.

3. **Determine the smallest exponent for the common prime factor:**
   - The smallest exponent of **2** in the factorizations is **2** (from 28 and 12).

4. **Calculate the GCF:**
   - GCF = 2² = **4**

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### **Method 2: Euclidean Algorithm**

1. **Find the GCF of two numbers first (e.g., 28 and 12):**
   - **28 ÷ 12 = 2** with a remainder of **4**
   - **12 ÷ 4 = 3** with a remainder of **0**
   - So, GCF(28, 12) = **4**

2. **Now, find the GCF of the result with the third number (4 and 24):**
   - **24 ÷ 4 = 6** with a remainder of **0**
   - So, GCF(4, 24) = **4**

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In both methods, the **greatest common factor** of **28**, **12**, and **24** is:

**4**
The greatest common factor of 28, 12, and 24 is 4.

Find the greatest common factor for the group of numbers. \( 28,12,24 \)

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