Most Efficient way to Compute the sum of divisors of N (1 ≤ N ≤ 1 000 000 000)

I want to write a code which computes the sum of divisors of a number N(1 ≤ N ≤ 1 000 000 000), excluding the number itself.

However, I need an efficient way to do it. It suppose to print the answer under 1 second. I know it depends on hardware etc. But I have an i7 machine though it takes more than a second (for the worst case scenario which is 1000000000 ) because of my poor code.

So to make it more understandable:

EX: Sample input: 10 --> Output should be: 8 (because we know 1 + 2 + 5 = 8)

EX: Input: 20 --> Output suppose to be: 22 ( 1 + 2 + 4 + 5 + 10 = 22 )

So far i wrote this:

public class Main
{
public static void main(String[] args)
{
    @SuppressWarnings("resource")
    Scanner read = new Scanner(System.in);

    System.out.print("How many times you would like to try: ");
    int len = read.nextInt();

    for(int w = 0; w < len; w++)
    {
        System.out.print("Number: ");
        int input = read.nextInt();

        int remains = 1;
        int sum = remains;

        /* All I know we only need to check half of the given number as 
           I learned ages ago. I mean (input / 2) :D */

        for(int i = 2; i <= input / 2; i++)
        {
            if(input % i == 0) sum += i;
        }

        System.out.print("Result: " + sum);
    }

}
}

So the question is How to improve this solution ? How to make it more efficient or let me put it this way. Is there a way to do it more efficient ?

If you could help me and show a solution code wise in Java, I would very appreciate it. Thanks for checking!