Question

The highest power of $2$ by which the product of first $100$ counting numbers can be divided without any remainder is $.......$

• A. $97$
• B. $96$
• C. $95$
• D. $94$

Answer 1

The correct option is A $97$

The highest power of a number x contained in n is
$[n\setminus x]+[n\setminus x^2]+[n\setminus x^3]+........tillbecomes0$
$n=100$
$x=2$
So total power$\Rightarrow [100\setminus 2]+[100\setminus 4]+[100\setminus 8]+[100\setminus 16]+[100\setminus 32]+[100\setminus 64]$
$\Rightarrow 50+25+12+6+3+1=97$
Hence, option 'A' is correct.