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

Guest Mar 28, 2021

#1**0 **

(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! :)

ArithmeticBrains1234 Mar 28, 2021