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Find the sum of the positive square free divisors of 54000.

Note: A natural number is square free if it is not the multiple of any perfect square greater than 1.

 
 Jan 12, 2021
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Are you sure that you want the "sum" or the "number" of  "free divisors of 54,000"?

 

54,000=(1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 100, 108, 120, 125, 135, 144, 150, 180, 200, 216, 225, 240, 250, 270, 300, 360, 375, 400, 432, 450, 500, 540, 600, 675, 720, 750, 900, 1000, 1080, 1125, 1200, 1350, 1500, 1800, 2000, 2160, 2250, 2700, 3000, 3375, 3600, 4500, 5400, 6000, 6750, 9000, 10800, 13500, 18000, 27000, 54000)>>Total = 80 divisors.

 

(1, 4, 9, 16, 25, 36, 100, 144, 225, 400, 900, 3600) >Total = 12 - these are perfect squares included in the above 80 divisors.

 

You simply remove these 11 perfect squares from the 80 divisors and sum up what is left.

 
 Jan 13, 2021

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