What is the GCF of 54 and \( 32 ? \)

To find the **Greatest Common Factor (GCF)** of 54 and 32, we can use the **Euclidean algorithm**, which is an efficient method for computing the GCF of two numbers. ### Step-by-Step Using the Euclidean Algorithm: 1. **Divide the larger number by the smaller number:** \[ 54 \div 32 = 1 \text{ with a remainder of } 22 \] So, \( 54 = 32 \times 1 + 22 \). 2. **Replace the larger number with the smaller number, and the smaller number with the remainder:** - Now, find the GCF of 32 and 22. 3. **Repeat the process:** \[ 32 \div 22 = 1 \text{ with a remainder of } 10 \] So, \( 32 = 22 \times 1 + 10 \). 4. **Continue:** \[ 22 \div 10 = 2 \text{ with a remainder of } 2 \] So, \( 22 = 10 \times 2 + 2 \). 5. **One more step:** \[ 10 \div 2 = 5 \text{ with a remainder of } 0 \] Since the remainder is now 0, the last non-zero remainder (**2**) is the GCF. ### Conclusion: The **GCF of 54 and 32 is 2**. **Answer:** The greatest common factor of 54 and 32 is 2.