The greatest common factor of 55/99 is 1 1.

The greatest common factor of 68/24 is 4.

The method is:

If the smaller number is reduced by 2 times, if the quotient obtained is a factor of the larger number, then this quotient is the greatest common factor of these two numbers.

If not, the smaller number is reduced by 3 times. If the quotient obtained is a factor of the larger number, this quotient is the greatest common factor of these two numbers.

By analogy, you can find it after several attempts.