+647 The product of a list of (not necessarily distinct) positive integers is 120. What is the least possible sum of the numbers in the list? What if the product were 144000? What is the least possible sum in this case?
+349 Not sure, but... for the 120 case, I guess it's 239? {120, 1, 1..., 1, 1}? Anyway, ask CPhill.
+129852 120 factors as 2^3 * 3 * 5 and the sum of these is
3(2) + 3 + 5 =
6 + 8
14
144000 factors as 2^7 * 3^2 * 5^3 and the sum of these is
7(2) + 2(3) + 3(5) =
14 + 6 + 15 =
35
+129852 First one
2* 2 * 2 * 3 * 5 = 8 * 3 * 5 = 24 * 5 = 120
Sum
2,2,2,3,5
2 + 2 + 2 + 3 + 5 = 14
Second one
2^7 * 3^2 * 5^3 = 144000
Sum
2,2,2,2,2,2,2,3,3,5,5,5
2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 5 = 35
+1713 I just didn't realize it... but heres the gist of my way thats basically the same as CPHILL I didn't get it at first because instead of 3^2 I thought it was 32...
The prime factorization of 144000 is2^7*3^2*5^3 , so the minimum sum in this case is 35 .
Thanks Melody and Cphill and mathhemath and waffles!
