Question

What is the HCF of two consecutive even numbers?

Answer 1

Take any 2 consecutive even numbers, One factor of each will be 2 & the other factor of both will be $2$ cosecutive natural numbers.. , in which one will be odd . like..

$2=2x1$

$4=2x2$

$6=2x3$

$8=2x4$

$32=2x16$

$34=2x17$

$36=2x18$

Since $2$ consecutive natural numbers have no common factor except $1$

So, HCF of $2$ even consecutive numbers $=2$