Question

What is the HCF of two consecutive even numbers?

Answer 1

Hint: Here we have to define what HCF of two consecutive numbers is. Later assume two consecutive even numbers, then find the factors of those numbers and find greatest common factors that divide the given number.

Complete step-by-step answer:
HCF of two consecutive even numbers,
Let 2n, (2n + 2) are two consecutive even numbers
$2n = 2 \times n$ …… (1)
$2n + 2 = 2\left( {n + 1} \right)$ …… (2)
Highest common factors is 2 from (1) and (2)
Let's check:
Let us assume that the two consecutive even numbers are 8 and 10,
We know that the factors of 8 and 10 are
8 – 1, 2, 4 and 8 …… (3)
10 – 1, 2, 5 and 10 …… (4)
Therefore from (1) and (2)
The highest common factor is 2
Hence the HCF of two consecutive even numbers is 2

Note: The HCF of two consecutive even numbers is the highest common factor that exists between the two numbers. We can also say that the greatest number that divides both the numbers is called HCF.