The number of members of the group must be a whole number, and each member paid the same whole dollar amount. Altogether they paid $299, so both the number of members and the price of the book must be factors of 299.
The factors of 299 are: 1, 13, 23, 299.
The only factor greater than 2 but less than 20 is 13, so that's the number of members. Each of them paid 299÷13=23 dollars.
There are 13 members in the club.