How many noughts are at the end of these giant numbers?
I have forgotten the number of the combination of the lock on my
briefcase. I did have a method for remembering it...
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
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.View the archive of all weekly problems grouped by curriculum topic