6th Grade Principle of Inclusion and Exclusion: Problem 1

Problem: Mr. Brown is a well-off farmer who is planning to pass down a part of his cattle to his three sons and younger brother. In all he has 2004 cows, each with a number labeled on them: 1~2004. He gives all of the cows whose label is a multiple of 2 to the eldest son, all of the cows whose label is a multiple of 3 to the middle son, and all of the cows whose label is a multiple of 5 to the youngest son. The rest of the remaining cows are given to Mr. Brown's brother. How many cows does Mr. Brown's brother get?

Key: Find the most central part of the venn diagram

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