Suppose that x and y are positive integers such that (2x)(3y) = 46656. What is the sum of all possible values of x?
+91 (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! :)
