Rebecca,

I'm not really sure how long the longest flare might have been. That is a difficult question to answer, since it depends on how you are measuring the flare. I can tell you that a flare that happened 21 Mar, 2011 (a C-class flare) lasted about fifteen hours. That is, the X-ray flux from the flare in one energy band took that long to return to its pre-flare level, as measured by an instrument in orbit around Earth on the GOES satellite. The first X-class flare of solar cycle 24 lasted only about an hour, however. If you would like to see the graphs yourself, go here:

http://www.swpc.noaa.gov/rt_plots/xray_5m.html

For information about flare classes, visit this website: