To find the highest common factor (HCF) of any two consecutive even numbers, we can start by defining what we mean by “consecutive even numbers.” These are numbers that are evenly spaced by 2. For example, if we take two consecutive even numbers like 4 and 6, or 10 and 12, we can find their HCF.
Let’s consider two consecutive even numbers: 2n and 2n + 2, where n is a whole number. The first number is always divisible by 2, and the second number is also divisible by 2.
To find the HCF, we can list the factors of both numbers:
- Factors of 2n: 1, 2, … , 2n
- Factors of 2n + 2: 1, 2, … , 2n + 2
It is apparent that the only common factor will be 2, since both numbers can be factored into multiples of 2. Any larger number would not divide both of the consecutive even numbers evenly due to their difference of 2.
For example, if we take consecutive even numbers 8 and 10:
- Factors of 8: 1, 2, 4, 8
- Factors of 10: 1, 2, 5, 10
The only common factor is 2. Therefore, the HCF of any two consecutive even numbers is always 2.