How to multiply two very big numbers without overflow ?

Question

Say I have given two big numbers i.e. 10^8 and 10^9 what could be the best way to multiply them without facing the overflow issue.

Answer 1

Multiply two numbers recursively to solve this problem using some mod function.. below is the code segment. We will multiply two numbers eg. calculate half of multiplication and then add it twice and then for calculating halt of multiplication of two num, calculate 1/4 and then add 4 times and so on...

long long  Multiply(long long a,long long b,long long mod)         
{
    long long  x ,y ;
    x=0;
    y= a % mod;
    while (b > 0)
    {
        if (b % 2 == 1)
        {    
            x = (x + y) % mod;
        }
        y = (y * 2) % mod;
        b /= 2;
    }
    return x % mod;
}