The factors of 55 are 1, 5, 11, and 55 .
The factors of 77 are 1, 7, 11, and 77 .
The factors that are common to both numbers are 1 and 11 .
The greatest one is 11 .
You asked for the "greatest", so you only get one of them. If there were
more than one greatest, then you'd want to know which greatest was
greater than the other greatest.