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

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: --- ### **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** --- ### **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** --- In both methods, the **greatest common factor** of **28**, **12**, and **24** is: **4**