I have forgotten the number of the combination of the lock on my
briefcase. I did have a method for remembering it...
Find the highest power of 11 that will divide into 1000! exactly.
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!?
The symbol $50!$ represents the product of all the whole numbers from 1 to 50 inclusive; that is, $50!=1 \times 2 \times 3 \times \dots \times 49 \times 50$. If I were to calculate the actual value, how many zeros would the answer have at the end?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.