When a mathematician says, “7 factorial”, they mean the product of all the integers from 1 up to and including 7. This is written with an exclamation mark:

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

In general, n! is the product of all the integers from 1 up to n:

n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1

Now we’re ready for this week’s problem:

1. Determine how many zeros there are on the end of the number 20!
2. Determine how many zeros there are on the end of the number 100!

If you can solve this problem, be proud: it is a classic Cambridge Mathematics interview question.