The largest natural number n such that 3^ n divides 66 ! is .....… - Vidyadip

MCQ

The largest natural number $n$ such that $3^{ n }$ divides $66 !$ is $............$.

A
$30$
✓
$31$
C
$32$
D
$33$

✓

Answer

Correct option: B.

$31$

b
${\left[\frac{66}{3}\right]+\left[\frac{66}{9}\right]+\left[\frac{66}{27}\right]}$

$22+7+2=31$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from binomial theoram→binomial theoram — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

${\log _4}18$ is

Minimum value of the function $f(x) = \left| {\sin \,x + \cos \,x + \tan \,x + \cot \,x + \sec \,x + \ cosec\ x} \right|$ is equal to

The straight line $x + 2y = 1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A, B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation, $x^2 +(2 - \lambda ) x+ (10 - \lambda ) = 0$ is minimum, then the magnitude of the difference of the roots of this equation is

The least remainder when ${17^{30}}$ is divided by $ 5$ is

The complex numbers $\sin x + i\cos 2x$ and $\cos x - i\sin 2x$ are conjugate to each other for

Write the inverse of the statement: If you do not drink your milk, you will not be strong.

The term independent of x in the expansion of $\Big(2\text{x}+\frac{1}{3\times2}\Big)^9.$

In the $X Y$-plane, three distinct lines $l_1, l_2, l_3$ concur at a point $(\lambda, 0)$. Further the lines $l_1, l_2, l_3$ are normals to the parabola $y^2=6 x$ at the points $A=\left(x_1, y_1\right)$, $B=\left(x_2, y_2\right), C=\left(x_3, y_3\right)$ respectively. Then, we have

The orthocentre of the triangle formed by $(0, 0),\, (8, 0), \,(4 6)$ is