What is the HCF of two consecutive even numbers?
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..
$$2 = 2 x 1$$
$$4 = 2 x 2$$
$$6 = 2 x 3$$
$$8= 2 x 4$$
$$32 = 2 x 16$$
$$34 = 2 x 17$$
$$36 = 2 x 18$$
Since $$2$$ consecutive natural numbers have no common factor except $$1$$
So, HCF of $$2$$ even consecutive numbers $$= 2$$