Back in my school days I was taught that a person could live for 3-4 weeks without food but with water; the teaching is still applicable… but there are other factors that dictates the surviving period.
Mental strength, health condition, body weight, climates and some other factors play their part in determining the survival length; under optimal circumstances a person could live without food for 6-8 weeks or even longer in extreme cases.
I am not sure if there’s any official record for the longest survival without food; the longest record that I managed to find is 73 days during the 1981 Irish hunger strike. A total of 10 prisoners had died after 46 to 73 days of starvation in the strike.
Laurence McKeown survived the strike for 70 days, which could be the record for the longest period for a person to live without food and still surviving.