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Find the sum of the positive square free divisors of 5400.

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

 Jun 24, 2020
 #1
avatar+980 
+1

5400 is 2^3 * 3^3 * 5^2 .

 

The square free divisors should be in the form 2^a * 3^b * 5^c... right?

 

Anyways so a, b, c, must be 0 or 1, since if it's 2 they would be a perfect square, 3, a perfect square times something.

 

So the sum should be (1+2)(1+3)(1+5).

 

Which is 72.

 

Tell me if AoPS says this is correct, please, because I think it is but I might be wrong.

 Jun 24, 2020
 #2
avatar+134 
+2

No, it says that its correct, thank you 

ItzMe  Jun 24, 2020
 #3
avatar+980 
+2

Ok great!

 

:)

hugomimihu  Jun 24, 2020

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