The product of 5 different integers is -80. What is the least possible sum?

Question

The product of 5 different integers is -80. What is the least possible sum? 

Answer 1

First consider 80. The factors of 80 are 1,2,4,5,8,10,16,20,40,80. What we'd like to do is find the largest 5 factors that multiply to 80, and sum them together. If we take the negative of those, they'll multiply to -80 since 5 factors means 5 negative numbers multiplied, which makes another negative negative (an even number of negative products is a positive number, an odd number of negative products is a negative number).