Question

$1.$ What is the HCF of two consecutive
(a) Numbers?
(b) Even numbers?
(c) Odd numbers?

$2.$ Find the HCF of the following :
$8$ and $12$

Answer 1

$1.$ (a) Let's take any two consecutive numbers as $4$ and $5$.
There is no common factor other than $1$ between $4$ and $5$.
Similarly, if we take any other two consecutive numbers, HCF will be $1$, only, as they are not having any common factor other than $1$.
Hence, HCF of two consecutive numbers will be $1$.

(b) Let's take any two consecutive even numbers as $6$ and $8$.
Prime factorization of $6$ and $8$
$6=2\times 3$
$8=2\times 2\times 2$
HCF of $6$ and $8$ is $2$.
Similarly, if we take any other two consecutive even numbers, HCF will be $2$ only, as they are multiple of $2$.
Hence, HCF of two consecutive even numbers will be $2$.
(c) Let's take any two consecutive odd numbers as $9$ and $11$.
Prime factorization of $9$ and $11$
$9=3\times 3$
$11=11$
HCF of $9$ and $11$ is $1$.
Similarly, if we take any other two consecutive odd numbers, HCF will be $1$ only, as they are not having any common factor other than $1$.
Hence, HCF of two consecutive odd numbers will be $1$.

$2.$ Lets find prime factorization of $8$ and $12$,
$8=2\times 2\times 2$
$12=2\times 2\times 3$

HCF of $8$ and $12=2\times 2=4$
Hence, HCF of $4$ and $12$ is $4$.