Question

Exponent of $12$ in $100!$ is

• A. $24$
• B. $48$
• C. $54$
• D. $36$

Answer 1

The correct option is B $48$

$12=2^2\times 3$

EXPONENT OF $2$ IN $100!$ IS

$=\left[\frac{100}{2}\right]+\left[\frac{100}{2^2}\right]+\left[\frac{100}{2^3}\right]+\left[\frac{100}{2^4}\right]+\left[\frac{100}{2^5}\right]+\left[\frac{100}{2^6}\right]$

$=50+25+12+6+3+1$

$=97$

EXPONENT OF $3$ IN $100!$ IS

$=\left[\frac{100}{3}\right]+\left[\frac{100}{3^2}\right]+\left[\frac{100}{3^3}\right]+\left[\frac{100}{3^4}\right]$

$=33+11+3+1$

$=48$

exponent of $12$ in $100!$ will be $48$