Question

The HCF of 2 consecutive even numbers is:
(a)0
(b)1
(c)4
(d)2

Answer 1

Hint: Find examples of even consecutive numbers. Find their common factor. Thus compare their common factor and find HCF, where HCF is the highest common factor.

Complete step-by-step answer:
HCF is the highest common factor. It can also be called as the greatest common divisor (gcd).
The gcd of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
The HCF is useful for reducing fractions to be in lowest terms.
Here we are asked to find HCF of 2 even consecutive numbers.
The even consecutive numbers are 2, 4, 6, 8, 12, 16 etc.
In case of two even consecutive numbers, the highest common factor is 2.
Now let us take example of it,
\[2=2\times 1\to \] common factor is 2.
\[4=2\times 2\to \] common factor is 2.
\[8=2\times 4\to \] common factor is 2.
\[16=2\times 8\] …… and so on.
Thus if we take any two even consecutive numbers, the greatest common factor is 2.
We can also take example, \[32=2\times 16\].
\[34=2\times 17\]
\[36=2\times 18\] and so on.
\[\therefore \] Option (d) is the correct answer.

Note: We can also take two consecutive even numbers as 2n and (2n + 2).
For, \[2n=2\times n\].
\[2n+2=2\times \left( n+1 \right)\].
Thus HCF (2n, 2n + 2) = 2.
The product of the smallest power of each common prime factor of the number, HCF is 2.