Efficient algorithm for finding a common divisor closest to some value?

Question

I have two numbers, x1 and x2. For a number y, I want to calculate the common divisor of x1 and x2 as close

Answer 1

1. Find the GCD of x1 and x2.
2. If GCD <= Y then return GCD
3. Current best answer is GCD, with a best distance of GCD - y.
4. Iterate through all numbers Y +/- [0 ... best distance]
5. Return the first integer that is a multiple of both x1 and x2

To find the GCD

public int getGCD( int a, int b )
{
   return (b==0) ? a : gcd(b, a%b);
}

To find closest divisor to y...

public int closestDivisor( int a, int b, int y ){
    int gcd = getGCD( a, b );
    if( gcd <= y ) return gcd;
    int best = gcd - y;
    for( int i = 0; i < best; i++ )
    {
        if( gcd % (i-y) == 0 ) return i - y;
        if( gcd % (i+y) == 0 ) return i + y;
    }
    return gcd;
}

I believe the only additional optimization available would be to factor the gcd (perhaps using a sieve?) as @trinithis suggested.