Hello, CalcBeginner!

Edit: Okay, you want the number-of-zeros for each factorial.

3) Find the number of 0's at the end of: .

Every factor-of-5 (together with a factor-of-2) contributes a zero to the end of the number.

How many factors-of-5 are in 1000-factorial?

Every 5th number has a factor-of-5: . fives.

But every 25th number has , each of which contributes another 5: . more fives.

And every 125th number has , each of which contributes yet another 5: . more fives.

And every 625th number has , each of which contributes yet another 5: . more five.

Therefore, 1000! contains factors-of-5,

. . . . . . . . and ends in 249 zeros.

How factors-of-5 are in 1001-factorial?

. . Using the same prodecure, we find the same number: 249 final zeros.

The same holds true for 1002-factorial, 1003-factorial and 1004-factorial.

. . Each has 249 final zeros.

We find that 1005! contains: . final zeros

So we have these answers: .