Three consecutive numbers.

Question

The product of three consecutive positive integers is 35,904. What is the sum of the three integers?

Answer 1

the simplest way to solve the problem, instead of using algebra, is to factor 35,904 as a product of prime factors

if you want, you can do the following:

x(x+1)(x+2)=35,904

x^3+3x^2+2x=35,904

x^3+3x^2+2x-35,904=0

any root of this equation must be a factor of 35,904 so you have to factor this number anyway

35,904=2*2*2*2*2*2*3*11*17

now rearrange the factors

(2*2*2*2*2)*(3*11)*(2*17)

32*33*34

32+33+34=99 is the answer