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Karlanna places 600 marbles into m total boxes such that each box contains an equal number of marbles. There is more than one box, and each box contains more than one marble. For how many values of m can this be done?

 Oct 31, 2018
 #1
avatar+17231 
+3

I just looked up all of the factors of 600:

 

1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600

 

Just count them up (but exclude '1' as there is more than one box) and 600 because there is more than one marble in each box.

 Oct 31, 2018
edited by ElectricPavlov  Oct 31, 2018
edited by ElectricPavlov  Oct 31, 2018
 #2
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+1

Hi EP: Here is a simple way for large numbers with many divisors:

Factor 600 =2^3 x 3^1 x 5^2 = Take the exponent of each: (3 + 1) x (1+1) x (2+1)=4 x 2 x 3=24 divisors.

 Oct 31, 2018

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