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 100 and 96, we look at their prime factorizations. For 100, the prime factorization is \(2^2 \times 5^2\), and for 96, it's \(2^5 \times 3\). The HCF is obtained by taking the lowest power of the common prime factors. The only common prime factor is 2. The lowest power of 2 present in both factorizations is \(2^2\). Therefore, the HCF is \(2^2 = 4\). So, the HCF of 100 and 96 is 4.