Factorials

Find the highest power of 11 that will divide into 1000! exactly.

6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

How many divisors does factorial n (n!) have?