Finding the highest common factor in a set of numbers

Question

Let M be the set of all nine-digit positive integers that contain each digit from 1 to 9 once. Find the highest common factor of all elements of M.

I understand the context of the question but I am not sure where to start or proceed. A step by step solution is needed.

Answer 1

Let $D$ the highest common factor of all elements of $M$.

Let $a \in M$. Then $9|a \Rightarrow D\ge9$

$\left(9|45=1+2+3+..+9\right)$

And $\gcd(123456789,123456798)=9\Rightarrow D\le9$

Hence, $D=9$