Which of the following statements is not true?

Options

A. The HCF of two distinct prime numbers is 1
B. The HCF of two co prime numbers is 1
C. The HCF of two consecutive even numbers is 2
D. The HCF of an even and an odd number is even.

Answer

To determine which statement is not true, we will analyze each option one by one.

### Step-by-Step Solution:

**Step 1: Analyze Option 1**
- Statement: The HCF of two distinct prime numbers is 1.
- Explanation: Prime numbers have only two factors: 1 and the number itself. For example, the prime numbers 3 and 5 have factors 1, 3 and 1, 5 respectively. Since they have no common factors other than 1, their HCF is indeed 1.
- Conclusion: This statement is **true**.

**Step 2: Analyze Option 2**
- Statement: The HCF of two co-prime numbers is 1.
- Explanation: Co-prime numbers are numbers that have no common factors other than 1. For example, 3 and 5 are co-prime. Their only common factor is 1, so their HCF is 1.
- Conclusion: This statement is **true**.

**Step 3: Analyze Option 3**
- Statement: The HCF of two consecutive even numbers is 2.
- Explanation: Consecutive even numbers can be represented as 2n and 2(n+1). For example, consider 2 and 4. The factors of 2 are 1 and 2, and the factors of 4 are 1, 2, and 4. The highest common factor is 2. This holds true for any pair of consecutive even numbers.
- Conclusion: This statement is **true**.

**Step 4: Analyze Option 4**
- Statement: The HCF of an even and an odd number is even.
- Explanation: Let's take an even number, say 2, and an odd number, say 3. The factors of 2 are 1 and 2, and the factors of 3 are 1 and 3. The only common factor is 1, which is odd. Therefore, the HCF is 1, not even. This statement is incorrect.
- Conclusion: This statement is **not true**.

### Final Answer:
The statement that is **not true** is: **The HCF of an even and an odd number is even.**

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