Grade 8 Mathematics Assignment Term one 2025 2.4. Rewrite 28 and 72 as a product of their prime factors Determine the HCF and LCM of 28 and 72 D. 2 ,

**Step 1: Prime Factorisation** - **For 28:** Write 28 as a product of primes: \[ 28 = 2 \times 14 = 2 \times 2 \times 7 = 2^2 \times 7 \] - **For 72:** Write 72 as a product of primes: \[ 72 = 8 \times 9 = 2^3 \times 3^2 \] **Step 2: Find the Highest Common Factor (HCF)** The HCF is found by taking the product of the common prime factors using the lowest exponents. - **Common prime factors:** Both 28 and 72 have the prime factor 2. - For 28: \(2^2\) - For 72: \(2^3\) The lowest power is \(2^2\). Thus, \[ \text{HCF} = 2^2 = 4 \] **Step 3: Find the Lowest Common Multiple (LCM)** The LCM is found by taking the product of all prime factors present in either number using the highest exponents. - **Prime factors and their highest powers:** - For 2: Highest power is \(2^3\) (from 72). - For 3: Present only in 72 as \(3^2\). - For 7: Present only in 28 as \(7^1\). Thus, \[ \text{LCM} = 2^3 \times 3^2 \times 7 = 8 \times 9 \times 7 = 504 \] **Final Answer:** - Prime factorisation: \[ 28 = 2^2 \times 7, \quad 72 = 2^3 \times 3^2 \] - HCF: \(4\) - LCM: \(504\)