Given two integer N or M find the number of zero’s trailing in product of factorials (N!*M!)?
Input : N = 4, M = 5 Output : 1 Explanation : 4! = 24, 5! = 120 Product has only 1 trailing 0. Input : N = 127!, M = 57! Output : 44
As discussed in number of zeros in N! can be calculated by recursively dividing N by 5 and adding up the quotients.
For example if N = 127, then
Number of 0 in 127! = 127/5 + 127/25 + 127/125 + 127/625
= 25 + 5 + 1 + 0
Number of 0s in N! = 31. Similarly, for M we can calculate and add both of them.
So, by above we can conclude that number of zeroes in N!*M! Is equal to sum of number of zeroes in N! and M!.
f(N) = floor(N/5) + floor(N/5^2) + … floor(N/5^3) + …
f(M) = floor(x/5) + floor(M/5^2) + … floor(M/5^3) + …
Then answer is f(N)+f(M)
- Count number of trailing zeros in product of array
- Product of first N factorials
- Count number of trailing zeros in Binary representation of a number using Bitset
- Check if a given number divides the sum of the factorials of its digits
- Count number of trailing zeros in (1^1)*(2^2)*(3^3)*(4^4)*..
- Count trailing zeroes in factorial of a number
- Number of trailing zeroes in base B representation of N!
- Smallest number divisible by n and has at-least k trailing zeros
- Number of trailing zeroes in base 16 representation of N!
- Find the smallest number X such that X! contains at least Y trailing zeros.
- Smallest number with at least n trailing zeroes in factorial
- Largest number with maximum trailing nines which is less than N and greater than N-D
- Count number of triplets with product equal to given number with duplicates allowed
- Sum and Product of digits in a number that divide the number
- GCD of factorials of two numbers
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : jit_t