Question

What is the HCF of two consecutive:
(a) natural numbers (b) even numbers (c) odd numbers​

Answer 1

your Answer

(a) two consecutive natural numbers

(b) two consecutive even numbers

(c) two consecutive odd numbers

(d) any two prime numbers

Answer 2

ᴀɴꜱᴡᴇʀ :-

ᴀꜱ ʟᴏɴɢ ᴀꜱ ɪ ʀᴇᴍᴇᴍʙᴇʀ

➡The HCF of two consecutive numbers is always one. The reason behind this is that the two

consecutive numbers do not have any common factor other than 1. Hence 1 becomes the

highest common factor between two consecutive numbers.

Now HCF of two consecutive even numbers is always two, we can prove it by taking two even numbers for example 18,20 both have only 2 as the common factor.

HCF of two consecutive odd numbers is always 1 ,as they do not have any common factor

other than 1.