Question

The HCF of two consecutive natural numbers is?
A) 0
B) 1
C) 2
D) Non existent

Answer 1

Hint: We can take some examples of two consecutive natural numbers (greater than 1), write down their factors and conclude what among them will be the highest common factors among them.
Factors are the numbers by the product of which the original number is obtained.

Complete step by step solution:
HCF is the highest common factor between the factors constituting the respective numbers that divides the two of them.
The numbers greater than 1 are called natural numbers.
Considering 9 and 10 as two consecutive (continuous) natural numbers, their factors are:
 $
\Rightarrow 9 = 1 \times 3 \times 3 \\
\Rightarrow 10 = 1 \times 2 \times 5 \;
  $
We can see that the only common factor among the two numbers is 1
Considering another example with 20 and 21 as the two consecutive (continuous) natural numbers, their factors are:
 $
\Rightarrow 20 = 1 \times 2 \times 5 \times 2 \\
\Rightarrow 21 = 1 \times 3 \times 7 \;
  $
We can see that the only common factor among the two numbers is also 1.
Thus it can be concluded that the highest common factor among the two consecutive natural numbers is 1.
This is because when we take continuous numbers greater than 1, one number will be even and other will be odd making the numbers co – prime .i.e. the common factor amongst them is 1
So, the correct answer is “OPTION B”.

Note: 1 is the factor of every number as all the numbers are divisible by 1. We have to consider the smallest possible specifically prime numbers as factors constituting the numbers. We can always find the common factors among the two known numbers as there will be some number by the product of which these are obtained (at least 2 i.e. 1 and the number itself), thus the option D) was eliminated automatically as the HCF will always exist.