Question

$3^r$ divides 50! then maximum value of r $=$

• A. $27$
• B. $25$
• C. $23$
• D. $22$

Answer 1

Answer: (D)

$22$

$\to$ Every $3^{rd}$ number has one power of 3 in it.
So, $n_1=\left[\frac{50}{3}\right]=16$ numbers have one 3 in them.
$\to$ Every $9^{th}$ number has 2 powers of 3, one of which has been counted earlier.
So, $n_2=\left[\frac{50}{9}\right]=5$ numbers have a second 3 in them.
$\to$ Every ${27}^{th}$ number has 3 powers of 3, 2 of which has been counted.
So, $n_3=\left[\frac{50}{27}\right]=1$
So, the Total no. of powers, r in 50!
= $\left[\frac{50}{3}\right]+\left[\frac{50}{9}\right]+\left[\frac{50}{27}\right]+$ ________
= 16+5+1
$r=22$