1. \( 100=2 \times 2 \times 5 \times 5=2^{2} \times 5^{2} \) \( 96=2 \times 2 \times 2 \times 2 \times 2 \times 3=2^{5} \times 3 \) \( H C F= \)

To find the **Highest Common Factor (HCF)** of the numbers **100** and **96**, let's break down each number into its prime factors and then identify the common factors. ### Step 1: Prime Factorization 1. **100** \[ 100 = 2 \times 2 \times 5 \times 5 = 2^{2} \times 5^{2} \] 2. **96** \[ 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^{5} \times 3 \] ### Step 2: Identify Common Prime Factors - **Common Prime Factor:** \(2\) ### Step 3: Determine the Lowest Exponent of the Common Prime Factor - For \(2\): - In **100**: exponent is **2** - In **96**: exponent is **5** **Lowest Exponent:** **2** ### Step 4: Calculate the HCF \[ \text{HCF} = 2^{2} = 4 \] ### Conclusion The **Highest Common Factor (HCF)** of **100** and **96** is **4**.