thats a difficult question to answer, 1 its been about 1000 years like Elveonora stated, there is 25 years for every 1 generation so that is 50 generations. but thats just a general usage of the termonology.
generally when talking about family when you say generation you mean you then your child and so on. the reason its difficult to answer is because 1 man can father a shat tonne of children.
and in 1000 years it would be very difficult to judge how many people had decended from asura. we also have to take into consideration how long shinobi can live if they are skilled or if they live a relatively peaceful life. it can be assumed that clans like the uchiha and senju had relatively short lives between those 1000 years because of the fact they were constantly at war with eachother. but it can be assumed that the senju lived longer lives since we know that they inherited asura's body, life force and stamina. and we know that the senju under hashirama's control consistantly won battles against the uchiha to the point that many uchiha simply gave up and went over to the side of the senju.
we can assume that since the uchiha and senju both had a good deal of members by the time of hashirama's life that this must mean they consistantly had children younger since they also would have died often in battle, which would require a consistant replacement fertility rate to stay alive with large numbers
meaning its safe to assume that in those 1000 years there were a lot more than 50 generations of senju born