What is the HCF of two consecutive even numbers?

The Highest Common Factor (HCF) of two consecutive even numbers is always 2.

Understanding HCF

The HCF, also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder.

HCF of Consecutive Even Numbers

Consider two consecutive even numbers:

• An even number can be represented as 2n, where 'n' is an integer.
• The next consecutive even number would be 2n + 2.

Let's analyze why the HCF is always 2:

• Both 2n and 2n + 2 are divisible by 2.
• We can rewrite 2n + 2 as 2(n + 1).
• Therefore, 2 is a common factor.
• Since they are consecutive even numbers, they won't share any larger common factors other than 2. Any other factor of 2n would not necessarily be a factor of 2n + 2.

Examples

Here are a few examples to illustrate this:

Even Number 1	Even Number 2	Factors of Even Number 1	Factors of Even Number 2	Common Factors	HCF
2	4	1, 2	1, 2, 4	1, 2	2
10	12	1, 2, 5, 10	1, 2, 3, 4, 6, 12	1, 2	2
24	26	1, 2, 3, 4, 6, 8, 12, 24	1, 2, 13, 26	1, 2	2

Conclusion

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