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Suppose that x and y are positive integers such that (2x)(3y) = 46656. What is the sum of all possible values of x?

 Mar 28, 2021
 #1
avatar+84 
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(2x)(3y) = 6xy

 

6xy = 46656

xy = 7776

 

So, essentially we are looking for two numbers(x and y) whose product is 7776.

 

Factor set of 7776: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776} 

 

For any of the factors of 7776, there is another number in that same factor set that when multiplied by the first factor, gives 7776.

Eg. 2*3888 = 7776

 

Thus the sum of the factor set of 7776 is your answer.

 

Sum of the factor set = 22932

 

Solved! :)

 Mar 28, 2021
edited by ArithmeticBrains1234  Mar 28, 2021
 #2
avatar+315 
+2

Wow good job!

wolfiechan  Mar 28, 2021

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