"bitwise and" operation between value and its two's component

Question

this operation uint256 pow2 = d & -d is from FullMath.sol

 function fullDiv(
        uint256 l,
        uint256 h,
        uint256 d
    ) private pure returns (uint256) {
        uint256 pow2 = d & -d;   
        d /= pow2;      
        .....
    }

I tested this operation with 20 and -20.

    00010100 = 20
    11101100 = -20

its bitwise and result is (If I am not mistaken so far)

 00010100 & 11101100=00000100

Why is this significant? Uniswap named variable AS pow2 but all the numbers from binary are already the power of 2. After the bitwise operation, d is divided by pow2=d & -d. I am trying to understand, what is the point of this division.

Answer 1

What is the importance of d /= pow2

The calculation uint256 pow2 = d & -d is the greatest power of 2 that divides d.

With d /= pow2 it is removing the zeros to the right. It is the "shifting" to the right both numerator and denominator. For example 51 / 20 = (51 / 4) / (20 / 4) = 12.75 / 5.

It is an optimization.