Question

The largest power of $2$ that divides $\frac{200!}{100!}$

• A. $98$
• B. $99$
• C. $100$
• D. $101$

Answer 1

The correct option is C $100$

In $200!$, highest power of $2$
$=\left[200/2\right]+\left[200/4\right]+\left[200/8\right]+\left[200/16\right]+\left[200/32\right]+\left[200/64\right]+\left[200/128\right]=100+50+25+12+6+3+1=197$

In $100!$, highest power of $2$
$=\left[100/2\right]+\left[100/4\right]+\left[100/8\right]+\left[100/16\right]+\left[100/32\right]+\left[100/64\right]=50+25+12+6+3+1=97$

Hence the highest power of $2$ that divides the number $=197-97=100$