Question

What is the HCF of two consecutive odd numbers?

Answer 1

Hint:- Odd numbers are not divisible by 2.
As, we all know that odd numbers are written in the form of \[2x \pm 1\].
And as we know that natural numbers are positive integers starting from 1.
So, the set of natural numbers is, \[\left( N \right) = \left\{ {1,2,3,4,5,......} \right\}\].
And, out all-natural numbers some are odd numbers and they were \[1,{\text{ }}3,{\text{ }}5,{\text{ }}7,......\]
As, we all know that HCF of two numbers will be the highest common factor of them.
But we can see that all consecutive odd numbers had only one common factor and that is 1.
Hence, HCF of two consecutive numbers will be 1.
Note:- Whenever we came up with this type of problem where we are not given with
particular number, then easiest and efficient way is to first write complete range of
that type of numbers and then select prove general result for all numbers in that range.