7:25 174 Done deltamath.com Assignment Overview 18 DeltaMath GCF/LCM (Division Algorithm) This is the only question in this section. Question Video Examples Find the greatest common factor and least common multiple of 32 and 144. Answer Attempt 1 out of 2 GCF: \( \square \) LCM: \( \square \) Submit Answer

Sure, I'd be happy to help you find the **Greatest Common Factor (GCF)** and the **Least Common Multiple (LCM)** of **32** and **144**. ### Step 1: Prime Factorization 1. **Factorizing 32:** \[ 32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5 \] 2. **Factorizing 144:** \[ 144 = 12 \times 12 \\ 12 = 2 \times 2 \times 3 = 2^2 \times 3 \\ \text{So, } 144 = (2^2 \times 3)^2 = 2^4 \times 3^2 \] ### Step 2: Finding the GCF The **GCF** is the product of the lowest powers of all common prime factors. - **Common Prime Factor:** 2 - **Lowest Power of 2:** \(2^4\) \[ \text{GCF} = 2^4 = 16 \] ### Step 3: Finding the LCM The **LCM** is the product of the highest powers of all prime factors present in either number. - **Prime Factors Needed:** 2 and 3 - **Highest Power of 2:** \(2^5\) - **Highest Power of 3:** \(3^2\) \[ \text{LCM} = 2^5 \times 3^2 = 32 \times 9 = 288 \] ### **Final Answers** - **GCF:** \(16\) - **LCM:** \(288\) So, you can fill in your assignment as follows: \[ \text{GCF: } 16 \] \[ \text{LCM: } 288 \]