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In a school, each student is assigned a positive factor of 6060, but no student's number is the greatest common divisor of any two student numbers (one of which may be their own).
What is the maximum number of students in this school?
An egg salesman was asked how many eggs he had sold that day. He replied, "My first customer said, 'I'll buy half your eggs and half an egg more'. My second and third customers said the same thing. When I had filled all three orders, I sold out of eggs without having to break a single egg the whole day."
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