……..is the HCF of two consecutive even numbers

Answer

To find the HCF (Highest Common Factor) of two consecutive even numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Define Consecutive Even Numbers**:
- Consecutive even numbers are two even numbers that follow each other. For example, let’s take 4 and 6 as our first pair of consecutive even numbers.

2. **Find the Prime Factorization**:
- **For 4**:
- 4 can be factored as \( 2 \times 2 \) or \( 2^2 \).
- **For 6**:
- 6 can be factored as \( 2 \times 3 \).

3. **List the Prime Factors**:
- The prime factors of 4 are \( 2, 2 \).
- The prime factors of 6 are \( 2, 3 \).

4. **Identify Common Factors**:
- The only common prime factor between 4 and 6 is \( 2 \).

5. **Determine the HCF**:
- Since the highest common factor is the largest factor that appears in both lists, the HCF of 4 and 6 is \( 2 \).

6. **Verify with Another Example**:
- Let’s take another pair of consecutive even numbers, 6 and 8.
- **For 6**: The prime factors are \( 2, 3 \).
- **For 8**: The prime factorization is \( 2 \times 2 \times 2 \) or \( 2^3 \).
- The prime factors of 8 are \( 2, 2, 2 \).
- The common factor here is still \( 2 \).
- Thus, the HCF of 6 and 8 is also \( 2 \).

7. **Conclusion**:
- From the examples, we can conclude that the HCF of any two consecutive even numbers is always \( 2 \).

### Final Answer:
The HCF of two consecutive even numbers is **2**.