Question

Find the HCF of two consecutive natural,even and odd numbers with full explanation?​

Answer 1

Answer:

Answer: The HCF of any two consecutive even numbers is always 2. The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.

Answer 2

Answer:

Case 1:

Consecutive Odd Numbers:

Let the first odd number be = 2k + 1 where k is some integer

and second one be 2k + 2 where k is some integer

HCF of consecutive odd numbers :

2k + 1 and 2k + 2

=> 2k + 1 = 2k + 1 ( it doesn't have any factors)

=> 2k+2 = 2(k + 1)

Therefore there are no common numbers other than 1

Therefore HCF of consecutive odd numbers is 1

Case 2:

Consecutive even numbers:

Let the first even number be 2k where k is some integer

2nd even number be = 2k + 2

HCF of consecutive even numbers:

=> 2k = 2*k

=> 2k + 2 = 2 (k+1)

Therefore they have 2 as common factor

Therefore HCF of consecutive even numbers is 2

Note : I have proven for Integer you can easily prove for natural by this method just try it and you can easily do it !

Hope you have understood.