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How many divisors of 5400 are not multiples of any perfect square greater than 1?

 

I know that there are 48 divisors of 5400 but I don't know how to figure out how many are not multiples of any perfect square greater than 1.

 Oct 22, 2021
 #1
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There are 6 divisors of 5400 that work.

 Oct 22, 2021
 #2
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Factors of 5400

All Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700 and 5400.

Count the black ones

 Oct 22, 2021

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