let x be the first number, then the next consecutive number is 1 more than that so it is x+1
product means multiply so x(x+1) = 4160
x^2 + x - 4160 = 0 factor this trinomial
(x+ 65 )(x-64 ) = 0
set each = 0 so x + 65=0 or x = -65 then x+1 = -64
x-64=0 so x=64 then x+1 = 65
since your question does specify positive or negative, then there are two possible answers 64 and 65 or -64 and -65