Factorials

problem
Factoring factorials

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

6! = 6 x 5 x 4 x 3 x 2 x 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!?
problem
Trailing zeros

Age

11 to 14

Challenge level

How many zeros does 50! have at the end?
problem
Factorised factorial

Age

14 to 16

Challenge level

Weekly Problem 17 - 2010
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?
problem
Seriesly

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

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