Question { Syntel, 9733 }

highest power of 25 that divides the product of the first
100 multiples of 5,74,100,62

Answer

The number in this case will be:
(5*1)*(5*2)..........(5*100)

So this number basically consists of 100 5s and (1*2*3...*100) which is 100!

Now we have to determine the power of 25 which will divide this number.
For this we will have to determine the number of 5s in the expression.

We know that there are 100 5s already.

Now consider 100!:

The number of zeros in 100! will be given by:

where [] is the greatest integer function
=> 20 + 4

So this will give 24 as the answer.

Now the total number of 5s are: 100+24 = 124

We need this number to be divisible by 125 which is :
5^2

So divide 124 by 2. This gives 62 as the answer.
So answer is 62