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How much zeros has the number $1000!$ at the end? If a number ends with n n zeros than it is divisible by 10n 10 n, that is 2n5n 2 n 5 n A factorial clearly has more 2 2 s than 5 5 s in its factorization so you only need to count how many 5 5 s are there in the factorization of 1000! 1000!
Find the number of times - Mathematics Stack Exchange Question: Find the number of times 5 5 will be written while listing integers from 1 1 to 1000 1000 Now, it can be solved in this fashion The numbers will be of the form: 5xy, x5y, xy5 5 x y, x 5 y, x y 5 where x, y x, y denote the two other digits such that 0 ≤ x, y ≤ 9 0 ≤ x, y ≤ 9 So, x, y x, y can take 10 10 choice each
combinatorics - How many numbers between $1000$ and $100000$ that do . . . Think of all the numbers between 1000 and 100,000 as five digit numbers (i e 1000 is actually 01000) How many numbers five digit numbers are there, well the short answer is 100,000 and we can arrive at this by saying that we have 10 choices for the first digit, and 10 for the second, etc to find that we have 105 = 100, 000 10 5 = 100, 000 numbers