154839

I believe the solution to the question is n=19.

I think this because if you subtract 144 and 220 by 11, you get 133 and 209.

Now we know that both 133 and 209 must both be able to be divided by n without any
reminders.

Factors of 133: 1,7,19,133
Facors of 209: 1,11,19,209

The highest common factor of 133 and 209 is 19.

And to double check, 144/19=7 R 11
220/19=11 R 11