Question

Find the largest integer n for which 35! Is divisible by 3n.

Solution

Correct option is

15

Let E(m) denote the exponent of 3 divides m. Then 

   .  

∴Largest value of n such that 3n divides 35! is 15.

SIMILAR QUESTIONS

Q1

Sum of all three digit numbers (no digit being zero) having the property that all digit are perfect squares, is

Q2

Let S = {1, 2, 3, ... n}. if X denote the set of all subsets of S containing exactly two elements, then the value of   

Q3

Let a be a factor of 120, then the number of integral solution of x1x2x3 = a is 

Q4

There are 15 points in a plane of which exactly 8 are collinear. Find the number of straight lines obtained by joining there points.   

Q5

If n is the number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any quation find n/40.

Q6

Find the number of rectangles that you can find on a chessboard.

Q7

Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9, no digit being repeated.

Q8

Ten persons, amongst whom are A, B and C, are to speak at a function. If n is the number of ways in which it can be done if A wants to speak before B, and B wants to speak before C find n/800.

Q9

Find the largest  such that 

      

Q10

The number of natural numbers which are smaller than 2 × 108 and which can be written by means of the digits and 2 is ………..