Question

find the H. C. F. of any two consecutive even numbers.

Answer 1

Answer:

H. C. F. of any two consecutive even numbers = 2

Step-by-step explanation:

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

2n = 2×n

2n+2 = 2(n+2) = 2×(n+2)

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

/* Product of the smallest power of each common prime factors of the numbers

Therefore,

H. C. F. of any two consecutive even numbers = 2

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Answer 2

Answer:

The HCF of two consecutive even numbers is 2.

Step-by-step explanation:

To find: HCF of any two consecutive even numbers

To find the solution let us consider that  

Let any two consecutive even numbers be 2a and 2a+2

Now let us find the HCF of the two even numbers which we have considered  

That is HCF of 2a and 2a+2

By finding the highest common factor

We get HCF of 2a and 2a+2 as 2

Hence the HCF any two consecutive even number is 2

Check:

To find HCF of 2, 4 where the two numbers are consecutive even numbers

Let us find the HCF of 2, 4

We get the factors as factors of 2 =2

Factors of 4 =2 x 2  

Hence 2 is the highest common factor of 2, 4

Hence verified