Which statement is not true?
HCF of two distinct prime numbers is 1.
HCF of two coprime numbers is 1.
HCF of two consecutive even numbers is 2.
HCF of an even and an odd number is even.
Goal: Find which statement is not true.
Check D: “HCF of an even and an odd number is even.”
• An even number is divisible by 2.
• An odd number is not divisible by 2.
So, 2 cannot be a common factor for an even and an odd number.
Therefore, their HCF cannot be even.
Example 1:
6 (even) and 9 (odd)
Factors of 6: \(1, 2, 3, 6\)
Factors of 9: \(1, 3, 9\)
Common factors: \(1, 3\)
HCF = \(3\) (which is odd)
Example 2:
8 (even) and 9 (odd)
Common factor is only \(1\)
HCF = \(1\) (which is odd)
Hence, statement D is false.
Quick check of the other statements:
A. Two distinct primes have only 1 as a common factor ⇒ HCF = \(1\) (true).
B. “Coprime” means HCF = \(1\) by definition (true).
C. Consecutive even numbers are \(2n\) and \(2n+2 = 2(n+1)\).
Both have a common factor 2, and no larger common factor.
Example: 6 and 8 → HCF = \(2\) (true).
Conclusion: The statement that is not true is D.