divide integer without remainder

Question

I have a set of numbers, where the total sum of them is always 1, I need to calculate the integer value that if divided on all those numbers the result will be without a remainder.

P.S: LCM won't work.

Any help?

Answer 1

I am going to assume "divided on" means "divided into". Suppose the sum of the numbers is $s$. If some integer $k$ divides each of the numbers without remainder then it must divide their sum without remainder too. So $s$ is a multiple of $k$. But we know $s=1$. So the only possible values for $k$ are $k= \pm 1$.