both the irish and the germans shared many push factors that drove them out of their home countries choose all that they share

Extreme poverty
Lack of jobs
The great Irish famine
Forced military service

Extreme poverty

Lack of jobs
The great Irish famine

Is that correct

Yes, that is correct. Both the Irish and Germans shared extreme poverty, lack of jobs, and the great Irish famine as push factors that drove them out of their home countries. Forced military service was not a significant factor for either group in this context.