Question

If $\left(a,0\right)=1$, what can$a$ possible be?

Short answer

The value of $a$ is $1$ or $-1$.

Step-by-step solution

Definition

According to the definition, if $a,b\ne 0$, then their greatest common divisor exists with a unique value. The greatest common divisor satisfies the condition $\left(a,b\right)\ge 1$, since 1 is the divisor of both $a,b$.

Find the value of  a

It is given that, $\left(a,0\right)=1$

According to the definition stated in step 1, any number can divide 0, so 1 is the greatest common divisor or integer which divides $a$.

Then $\left|a\right|=1$, which implies, $a=\pm 1$.

Hence, the value of is $1$ or $-1$.