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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?

waffles  Oct 19, 2017
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2+0 Answers

 #1
avatar+302 
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Not sure, but... for the 120 case, I guess it's 239? {120, 1, 1..., 1, 1}? Anyway, ask CPhill.

Mathhemathh  Oct 19, 2017
 #2
avatar+78557 
+1

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

 

 

cool cool cool

CPhill  Oct 19, 2017

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