Question

For $25!$, the correct options is/are

• A. exponent of $2$ is $22$
• B. exponent of $3$ is $10$
• C. exponent of $4$ is $7$
• D. exponent of $7$ is $3$

Answer 1

Answer: (A), (B), (D)

exponent of $7$ is $3$

Exponent of $2$ is
$\left[\frac{25}{2}\right]+\left[\frac{25}{2^2}\right]+\left[\frac{25}{2^3}\right]+\left[\frac{25}{2^4}\right]+\left[\frac{25}{2^5}\right]+...=12+6+3+1=22$
Exponent of $3$ is
$\left[\frac{25}{3}\right]+\left[\frac{25}{3^2}\right]+\left[\frac{25}{3^3}\right]+...=8+2=10$

Exponent of $2$ is $22$
$\Rightarrow$ Exponent of $2^2$ is $11$
$\Rightarrow$ Exponent of $4$ is $11$

Exponent of $7$ is
$\left[\frac{25}{7}\right]+\left[\frac{25}{7^2}\right]+...=3$