The HCF and LCM of 96 and 404 respectively are :

Question

Accepted Answer

To determine the correct answer for the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of 96 and 404, we need to perform the following calculations:

1. **Finding the HCF:**
   - The HCF of two numbers is the largest number that divides both of them without leaving a remainder.
   - Prime factorization of 96: $96 = 2^5 \times 3^1$
   - Prime factorization of 404: $404 = 2^2 \times 101^1$
   - The common prime factor is 2, and the smallest power of 2 common to both factorizations is $2^2$.
   - Therefore, the HCF of 96 and 404 is $2^2 = 4$.

2. **Finding the LCM:**
   - The LCM of two numbers is the smallest number that is a multiple of both.
   - Using the prime factorizations:
     - For 96: $2^5 \times 3^1$
     - For 404: $2^2 \times 101^1$
   - The LCM is found by taking the highest power of all prime factors present in either number:
     - Highest power of 2: $2^5$
     - Highest power of 3: $3^1$
     - Highest power of 101: $101^1$
   - Therefore, the LCM is $2^5 \times 3^1 \times 101^1 = 32 \times 3 \times 101 = 9696$.

Based on these calculations, the HCF is 4 and the LCM is 9696, which corresponds to Option 2.

**Explanation of why other options are incorrect:**

- **Option 1: 2 and 6969**
  - The HCF is incorrectly stated as 2. The correct HCF is 4.
  - The LCM is incorrectly stated as 6969. The correct LCM is 9696.

- **Option 3: 2 and 5446**
  - The HCF is incorrectly stated as 2. The correct HCF is 4.
  - The LCM is incorrectly stated as 5446. The correct LCM is 9696.

- **Option 4: 2 and 9696**
  - The HCF is incorrectly stated as 2. The correct HCF is 4.
  - The LCM is correctly stated as 9696, but since the HCF is incorrect, this option is not correct.

Thus, Option 2 is the only option that correctly states both the HCF and LCM of 96 and 404 as 4 and 9696, respectively.