Final answer:
Jeremey can pass out materials to a maximum of 16 classrooms. Each class will receive 5 flyers and 4 buttons each.
Step-by-step explanation:
To determine the greatest number of classrooms Jeremey can pass out materials to, we need to find the greatest common divisor (GCD) of 80 and 64. The GCD of 80 and 64 is 16. Therefore, Jeremey can pass out materials to a maximum of 16 classrooms. Each class will receive 80/16 = 5 flyers and 64/16 = 4 buttons each.