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.
Answers
Answer:
C)The HCF of two consecutive even numbers is 2.
Answer:
The correct answer is option (D) The HCF of an even and an odd number is even.
Step-by-step explanation:
Option (A) The HCF of two distinct prime numbers is 1.
Prime numbers have only two factors, i.e., 1 and the number itself. So, if we talk about H.C.F. (Highest common factor) of any two prime numbers, then the only factor left is 1. Hence, the statement is true.
Option (B) The HCF of two co prime numbers is 1
The statement is true because two prime numbers have only one factor, i.e., 1 and it will be their only highest common factor.
Option (C) The HCF of two consecutive even numbers is 2
Even numbers are those numbers which are divisible by 2.
If we talk about two consecutive even numbers, then their highest common factor will be only 2 and hence, the statement is true.
For example: H.C.F. of 4 and 6 is 2, H.C.F. of 6 and 8 is also 2.
Option (D) The HCF of an even and an odd number is even.
This statement is not true because the HCF of an even and an odd number can be odd also.
Hence, the correct answer is option (D).
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