## Question

Find the number of zeroes in 100!

### Solution

24

We know, 10 = 5 × 2.

So, to form one 10, we need one 2 and one 5.

Number of 10’s will be same as min{*E*_{2}(100!), *E*_{5}(100!)}

.

.

.

#### SIMILAR QUESTIONS

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

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.

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

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.

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.

Find the largest such that

Find the largest integer n for which 35! Is divisible by 3* ^{n}*.

The number of natural numbers which are smaller than 2 × 10^{8} and which can be written by means of the digits and 2 is ………..

Find the exponent of 2 in 50!?

A city has 12 gates. In how many ways can a person enter the city through one gate and come out through a different gate?