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Question

The largest power of 2 that divides 200!100!
  1. 99
  2. 98
  3. 101
  4. 100


Solution

The correct option is D 100

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

Hence the highest power of 2 that divides the number =19797=100

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