What is the largest power of 2 that divides 200!/100!.
No use of calculator is allowed. I had proceeded in a brute force method which i know regret.. I would like to know your methods.
Answer
Find highest power of 2 in 200! and 100!, using Legendre's formula
In 200!, highest power of 2
=⌊200/2⌋+⌊200/4⌋+⌊200/8⌋+⌊200/16⌋+⌊200/32⌋+⌊200/64⌋+⌊200/128⌋
=100+50+25+12+6+3+1=197
In 100!, highest power of 2
=⌊100/2⌋+⌊100/4⌋+⌊100/8⌋+⌊100/16⌋+⌊100/32⌋+⌊100/64⌋
=50+25+12+6+3+1=97
Now, just subtract the two, and we get 100 as the answer.
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