Quick HCF

$12345678987654321=111111111^2$ and $12345654321=111111^2$

The GCD of 1 $11111111$ and $111111$ is $111$ , which you can get easily from the Euclidean Algorithm

( $111111111-111111*1000=111$ and $111$ divides both $111111111$ and $111111$ ).

Therefore, the GCD of $12345678987654321=111111111^2$ and $12345654321=111111^2$ is $111^2=\boxed{12321}$