To find out how many students answered football as their favorite sport, we need to calculate 3 out of every 7 of the 150 students surveyed.
We can set up the calculation as follows:
\[ \text{Number of students who favor football} = \left(\frac{3}{7}\right) \times 150 \]
Calculating this gives:
\[ \frac{3 \times 150}{7} = \frac{450}{7} \approx 64.2857 \]
Since we are asked to round down our answer, we take the integer part of this number, which is 64.
Therefore, the most reasonable number of students who answered football as their favorite sport is:
\[ \boxed{64} \]