exponents and Power

guerrero wrote:If N is the product of all multiples of 3 between 1 and 100, what is the greatest integer m for which N/10^m is an integer?

For N/10^m to be an integer, 10^m must divide N.

Now, 10^m is a power 10.
So, if N is divisible by 10^m, N must contain m number of 10s, i.e. m number of 2s and 5s.

Now, as N = product of all multiples of 3 between 1 and 100, there will be more 2s than 5s in N.
So, it is easier for us to calculate the number of 5s in N.

Number of 5s in N = Number of 5s in 15, 30, 45, 60, 75, and 90 = 1 + 1 + 1 + 1 + 2 + 1 = 7

So, N at the most contain seven 5s.
--> N at the most will be divisible by 10^7.
--> Greatest value of m is 7.

The correct answer is C.