Question

If HCF of $m$ and $n$ is $1,$ then what are the HCF of $m+n,m$ and HCF of $m-n,n$ respectively?

$(m>n)$

• A. $1$ and $2$
• B. $2$ and $1$
• C. $1$ and $1$
• D. cannot be determined

Answer 1

The correct option is C $1$ and $1$

Let us consider an example.

Let $m=16$ and $n=9$ be relatively prime numbers.
So, $m+n=25$. The HCF of $25$ and $16$ is $1$.
$m-n=7$. The HCF of $7$ and $9$ is $1$.

Similarly, if we take other values for $m$ and $n,$ we get the same answer.
Therefore, option $C$ is correct.