Doubt in Foundation Quiz Gregmat Website

GRE Quant Problem Solving
1

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I did this by finding out the highest power of 2. And getting the answer as A. Is the approach wrong?

2

What does “highest power of 2” mean? Explain further.

3

4^100= 2^200 and counting total no. of factors of 2 in 100!.

I figured out my mistake. Thanks