Question

H.C.F. of two consecutive even numbers is :

• A. $0$
• B. $1$
• C. $4$
• D. $2$

Answer 1

Answer: (D)

$2$

Consider two consecutive even numbers. They are of the form $2n,2n+2$ for some integer n

$2n=2\times n$

$2n+2=2\times (n+1)$

The numbers $n,n+1$, being two consecutive integers, are relatively prime

They do not have any factor other than $1$ common to them.

Hence HCF of two consecutive even numbers is $2$.

So the correct answer is option D