You are given the following information. \[ 252=2 \times 2 \times 3 \times 3 \times 7 \quad 360=2 \times 2 \times 2 \times 3 \times 3 \times 5 \] 4.3 .1 Determine the bighest common factor (HCF) of 252 and 360 .

To determine the **Highest Common Factor (HCF)** of **252** and **360**, let's analyze their prime factorizations: \[ \begin{align*} 252 &= 2 \times 2 \times 3 \times 3 \times 7 \quad \text{or} \quad 2^2 \times 3^2 \times 7 \\ 360 &= 2 \times 2 \times 2 \times 3 \times 3 \times 5 \quad \text{or} \quad 2^3 \times 3^2 \times 5 \\ \end{align*} \] **Steps to find the HCF:** 1. **Identify Common Prime Factors:** - Both numbers share the prime factors **2** and **3**. 2. **Choose the Lowest Exponent for Each Common Factor:** - For **2**: - 252 has \(2^2\) - 360 has \(2^3\) - **Choose \(2^2\)** - For **3**: - Both have \(3^2\) - **Choose \(3^2\)** 3. **Multiply the Chosen Factors:** \[ \text{HCF} = 2^2 \times 3^2 = 4 \times 9 = 36 \] **Conclusion:** The **HCF of 252 and 360 is 36**.