 # Find the HCF of any two consecutive even numbers.

Highest Common Factor is the largest common divisor or gcd of two or more positive integers, as the mathematics rules dictate, appears to be the largest positive integer that divides the numbers without leaving a remainder.

Example:

Consider the two number 8 and 12.

As the highest number that can divide both 8 and 12 is 4.

Therefore, the H.C.F. of 8 and 12 would be 4.

The HCF o two consecutive numbers are always one. The reason behind this is that the two consecutive numbers do not have any common factor other than 1. Hence 1 becomes the highest common factor between two consecutive numbers.

HCF of any two consecutive even numbers is 2.

Let us consider two consecutive numbers 2b and (2b+2).

2b = 2 × b

2b + 2 = 2(b + 2) = 2 × (b + 2)

HCF of (2b, 2b+2) = 2

2n,(2n+2) are two consecutive even Numbers.

2n = 2×n

2n+2 = 2(n+2) = 2×(n+2)

HCF(2n,2n+2)= 2

Let us verify the above statment.

To find HCF of 2, 4

Let us find the Highest Common Factor of 2, 4

We get the factors as factors of 2 =2

Factors of 4 =2 x 2

HCF of (2, 4) = 2