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Q.

What is the HCF of two consecutives even numbers?


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a

1

b

2

c

3

d

4

answer is B.

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Detailed Solution

Consider the even number 2n  , where n can be any integer. By the property, “the two consecutives even numbers differ by 2”.
Now, using the above two statements, we get
The number is 2n+2  , which can be written as 2(n+1)  .
Thus, the two consecutive numbers are 2n   and 2(n+1)  .
Now, we can see that the above two consecutive numbers share a factor of 2. We also know that the HCF of two numbers is the number that is common in both number’s factors.
By using the above two statements, we conclude that 2   is a factor in both consecutive even numbers, 2n   and 2(n+1)  .
Hence, the correct option is 2.
 
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