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Which of the following statements is not true? 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.?
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Which of the following statements is not true? a)The HCF of two distin...
Explanation:
Statement a: The HCF of two distinct prime numbers is 1
This statement is true. This is because the only factor that two distinct prime numbers have in common is 1. Hence, the HCF of two distinct prime numbers is always 1.
Statement b: The HCF of two co prime numbers is 1
This statement is also true. Co-prime numbers are those numbers which have no common factors other than 1. Hence, the HCF of two co-prime numbers is always 1.
Statement c: The HCF of two consecutive even numbers is 2
This statement is true. This is because any two consecutive even numbers have a common factor of 2. Hence, the HCF of two consecutive even numbers is always 2.
Statement d: The HCF of an even and an odd number is even
This statement is not true. The HCF of an even and an odd number can be either even or odd. For example, the HCF of 6 and 9 is 3, which is odd. However, the HCF of 8 and 12 is 4, which is even. The HCF can be either even or odd depending on the numbers involved.
Conclusion: In conclusion, all the statements except statement d are true. The HCF of two distinct prime numbers is always 1, the HCF of two co-prime numbers is always 1, and the HCF of two consecutive even numbers is always 2. However, the HCF of an even and an odd number can be either even or odd.
Statement a: The HCF of two distinct prime numbers is 1
This statement is true. This is because the only factor that two distinct prime numbers have in common is 1. Hence, the HCF of two distinct prime numbers is always 1.
Statement b: The HCF of two co prime numbers is 1
This statement is also true. Co-prime numbers are those numbers which have no common factors other than 1. Hence, the HCF of two co-prime numbers is always 1.
Statement c: The HCF of two consecutive even numbers is 2
This statement is true. This is because any two consecutive even numbers have a common factor of 2. Hence, the HCF of two consecutive even numbers is always 2.
Statement d: The HCF of an even and an odd number is even
This statement is not true. The HCF of an even and an odd number can be either even or odd. For example, the HCF of 6 and 9 is 3, which is odd. However, the HCF of 8 and 12 is 4, which is even. The HCF can be either even or odd depending on the numbers involved.
Conclusion: In conclusion, all the statements except statement d are true. The HCF of two distinct prime numbers is always 1, the HCF of two co-prime numbers is always 1, and the HCF of two consecutive even numbers is always 2. However, the HCF of an even and an odd number can be either even or odd.
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Which of the following statements is not true? a)The HCF of two distin...
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Which of the following statements is not true? 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.? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which of the following statements is not true? 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.? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is not true? 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.?.
Which of the following statements is not true? 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.? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which of the following statements is not true? 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.? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is not true? 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.?.
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