Number Splitting

It might be a bit hard to notice, but $3360=15^3-15$ . Now, we go to the form $x^3-x$ Which upon factorisation, becomes $(x)(x+1)(x-1)$ . These happen to be consecutive numbers, thus we only need to find the sum of 15-1, 15 and 15+1. This leads to the answer of $\boxed{45}$ .

I did it the following way: 3360 = 2X3x4x4X5X7= 14X15X16 14+15+16 =45

X (X+1) (X+2)=3360 => X=14 So, X+1=15 & X+2=16 Sum= 14+15+16=45 So, Answer: 45...

3360^1/3=14.9777
so consecutive numbers are 14,15 & 16
14+15+16=45

I suggest trial and error method. Since the numbers are ascending just think of a number that will fit the description. On trying, start on number 10 as value for X, then try the other.

Let the first term be X then the next term be (X+1),(X+2) Now X (X+1) (X+2)=3360 We get X =14 and next two terms are 15,16 14+15+16=45

Well I solved it in the following way.

First I took the prime factorisation of 3360

Next I found the factors of 3360

Upon finding the factors I found that the three consecutive factors were 14,15 and 16

Therefore 14+15+16=45