# 1*2*3*4*5*6.....upto 1000 Find the number of zeroes at the end?

##### 1 Answer

#### Explanation:

This product is commonly known as the factorial of

The number of zeros is determined by how many times

There are plenty of factors of

These numbers have at least one factor

#5, 10, 15, 20, 25,..., 1000# which is#1000/5 = 200# numbers.

These numbers have at least two factors

#25, 50, 75, 100,..., 1000# which is#1000/25 = 40# numbers.

These numbers have at least three factors

#125, 250, 375, 500,..., 1000# which is#1000/125 = 8# numbers

This number has four factors

#625# which is#1# number.

So the total number of factors

#200+40+8+1 = 249#

Hence there are