Find the HCF of any Two Consecutive Even Numbers

Q. Find the HCF of any two consecutive even numbers

ANSWER: 2 Even Numbers in a Row: Even numbers are those that conclude in 0, 2, 4, 6, or 8. The following are some examples of successive even numbers: 0, 2, 4, 6, 8, 10

The (GCD) greatest common divisor is the largest positive integer that divides every one of two or more numbers that are not all zero in mathematics.

The adjective “greatest” can be substituted by “highest,” and the word “divisor” by “factor,” resulting in different names such as (HCF) highest common factor, and so on.

Other titles for the same notion in the past have included the largest common measure and greatest common factor.

The highest common divisor, or (HCF), of two or more positive numbers is the greatest positive number that divides the integers without leaving a remainder, as the arithmetic rules indicate.

Assume ‘2k’ and ‘2k+2’ are two consecutive even numbers.

Factor the numbers as follows:

2k=2*K

2k+2 = 2* (k+1) 

The number 2 is the largest common factor of the numbers ‘2k’ and ‘2k+2.’

Consider the numbers 4 and 6, which are consecutive even numbers.

4 and 6 have an HCF of 2.

Assume ‘2k’ and ‘2k+2’ are the two consecutive even numbers.

Any two consecutive even integers have the same HCF, which is always 2.