304 The results of factorizing prime factors are 2,2,2,2, 19.
In 2008, four twos were multiplied to get 16, but the father could not be 19 years old. Then it can only be multiplied by three twos, and the father's age is 38, which means 8*38=304.
In 2007, the child was 7 years old and the father was 37 years old.