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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.
Correct answer is option 'D'. Can you explain this answer?
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Which of the following statements is not true?a)The HCF of two distinc...
Explanation:
HCF stands for Highest Common Factor. It is the highest number that divides two or more numbers exactly. Let's examine each statement to determine which one is not true.
HCF of two distinct prime numbers is 1
- This statement is true because prime numbers only have 1 and itself as factors. Therefore, they cannot have any other common factor except 1.
HCF of two co-prime numbers is 1
- This statement is also true because co-prime numbers are those numbers that do not have any common factor except 1.
HCF of two consecutive even numbers is 2
- This statement is true because every even number is divisible by 2. So, the HCF of two consecutive even numbers will be 2.
HCF of an even and an odd number is even
- This statement is not true. Let's take an example to understand why. Suppose we have two numbers, 12 and 15. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 15 are 1, 3, 5, and 15. The common factors of 12 and 15 are 1 and 3. Therefore, the HCF of 12 and 15 is 3, which is odd. Hence, the statement is not true.
Therefore, the correct answer is option D, i.e., the HCF of an even and an odd number is not always even.
HCF stands for Highest Common Factor. It is the highest number that divides two or more numbers exactly. Let's examine each statement to determine which one is not true.
HCF of two distinct prime numbers is 1
- This statement is true because prime numbers only have 1 and itself as factors. Therefore, they cannot have any other common factor except 1.
HCF of two co-prime numbers is 1
- This statement is also true because co-prime numbers are those numbers that do not have any common factor except 1.
HCF of two consecutive even numbers is 2
- This statement is true because every even number is divisible by 2. So, the HCF of two consecutive even numbers will be 2.
HCF of an even and an odd number is even
- This statement is not true. Let's take an example to understand why. Suppose we have two numbers, 12 and 15. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 15 are 1, 3, 5, and 15. The common factors of 12 and 15 are 1 and 3. Therefore, the HCF of 12 and 15 is 3, which is odd. Hence, the statement is not true.
Therefore, the correct answer is option D, i.e., the HCF of an even and an odd number is not always even.
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Which of the following statements is not true?a)The HCF of two distinc...
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Which of the following statements is not true?a)The HCF of two distinct prime numbers is 1b)The HCF of two co prime numbers is 1c)The HCF of two consecutive even numbers is 2d)The HCF of an even and an odd number is even.Correct answer is option 'D'. Can you explain this answer?
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