Amanda is organizing a dinner party for a group of friends. He has prepared 45 chicken dumplings and 75 shrimp wantons. He manages to split the chicken dumplings and shrimp wantons evenly amongst everyone, so that everyone got the same number of chicken dumplings as each other, and similarly for the shrimp wantons. What is the most number of people that could be at the party?

gcf of 75 and 45 = 15