Modifying the locker problem

Level pending

A boy enters school to see \(5100\) lockers opened. He was tasked by his teacher to close all of the lockers. Being a very bored person, he decides to close them in a peculiar manner. First, he closes all lockers that are multiples of \(2!\), then, he closes all lockers that are multiples of \(3!\), however, if the locker is already closed, he opens it. He repeats this for \(4!\), \(5!\), \(6!\) and lastly \(7!\). How many lockers would still be open?

My apologies, I posted this question previously with the wrong answer

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