Which of the following statement is correct
(a) Two distinct prime numbers are always coprime but converse is not true.
(b) Coprime number are those whose HCF is one.
(c) Any two consecutive Natural numbers are not always coprime
(d) None of these

Let's analyze each of the statements:

**(a) Two distinct prime numbers are always coprime but converse is not true.**  
This statement is correct. Two distinct prime numbers are always coprime because their only common factor is 1. The converse, however, is not true because two numbers being coprime does not necessarily mean they are prime. For example, 8 and 9 are coprime, but neither is a prime number.

**(b) Coprime numbers are those whose HCF is one.**  
This statement is also correct. By definition, two numbers are coprime if their highest common factor (HCF) is 1.

**(c) Any two consecutive natural numbers are not always coprime.**  
This statement is incorrect. Any two consecutive natural numbers are always coprime because the only common divisor they can have is 1.

**(d) None of these.**  
This option is incorrect because statements (a) and (b) are correct.

**Correct Answer: (a) and (b)**

Since you need to pick one, the most generally applicable correct answer is **(d) None of these**, because the multiple-choice format usually implies only one correct answer, and multiple answers are correct here. However, if only one correct statement is required, I'd pick **(b)** as the most straightforward correct option. 

Would you like details or have any questions? 

Here are five related questions for you:

1. What is the difference between prime numbers and coprime numbers?
2. Can two composite numbers be coprime?
3. How do you find the HCF of two numbers using the Euclidean algorithm?
4. Why are consecutive natural numbers always coprime?
5. What is the significance of coprime numbers in number theory?

**Tip:** When identifying coprime numbers, remember that they don’t have to be prime themselves; they just need to have no common factors other than 1.

Explore the concepts of coprime numbers and prime numbers with detailed explanations. Understand why two distinct prime numbers are always coprime, the definition of coprime numbers, and more. Suitable for students in Grades 7-9.

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