7:24 174 Done deltamath.com Assignment Overview 19 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 80 and 200. Answer Attempt 1 out of 2 GCF: \( \square \) LCM: \( \square \) Submit Answer

Sure, let's find the **Greatest Common Factor (GCF)** and **Least Common Multiple (LCM)** of **80** and **200**. ### Step 1: Prime Factorization 1. **Factorize 80:** - \(80 = 2 \times 40\) - \(40 = 2 \times 20\) - \(20 = 2 \times 10\) - \(10 = 2 \times 5\) So, \(80 = 2^4 \times 5^1\) 2. **Factorize 200:** - \(200 = 2 \times 100\) - \(100 = 2 \times 50\) - \(50 = 2 \times 25\) - \(25 = 5 \times 5\) So, \(200 = 2^3 \times 5^2\) ### Step 2: Find the GCF The **GCF** is found by multiplying the lowest powers of all common prime factors. - **Common prime factors:** 2 and 5 - **Lowest powers:** - For 2: \(2^3\) - For 5: \(5^1\) \[ \text{GCF} = 2^3 \times 5^1 = 8 \times 5 = 40 \] ### Step 3: Find the LCM The **LCM** is found by multiplying the highest powers of all prime factors involved. - **Prime factors:** - For 2: \(2^4\) - For 5: \(5^2\) \[ \text{LCM} = 2^4 \times 5^2 = 16 \times 25 = 400 \] ### **Final Answers:** - **GCF:** 40 - **LCM:** 400