Question

Find the HCF of any two consecutive even numbers.

Answer 1

Find the HCF of two consecutive even numbers

We know that any even number is of the form $2k$ where $k$ is integer.

The even number next to $2k$ is $2k+2$, which can be written as $2(k+1)$

$k$and $k+1$ are consecutive numbers and any two consecutive numbers have HCF $1$.

So, $k$and $k+1$ has no common factors, and the only common factor of $2k$ and $2(k+1)$ is $2$

Hence, the Highest Common Factor of $2k$ and $2(k+1)$ is $2$

Hence, the HCF of any two consecutive even numbers is $2$