Answer
10 octaves. 7 octaves plus a minor third (A0 to C8).
Work Step by Step
If you multiply the frequency of a note by 2, you have the same note, but in the next higher octave.
A young person with undamaged hearing can detect sounds with frequencies from 20-20,000 Hz. This is a factor of about 1000. Ten doublings of frequency gives a factor of $2^{10} = 1024$, which is about 1000. So, normal human hearing spans about 10 octaves.
You can look at the keyboard of an 88-key piano and count a little more than 7 octaves: to be persnickety, a piano keyboard contains 7 octaves plus a minor third (A0 to C8).
