I assumed that the answer would be five due to the fact that it is possible to divide T by 3, 4 (2X2), and 5. Then, if we divide a group by 6 (3x2), the remaining divisor should be 5. Is this way of thinking flawed in any way?

What is T?

Sorry, T would be the total number of members

T does not divide by 3 - it has remainder 3 when divided by 4.