## Task 5 - 030715

How many zeros does the product of all natural numbers from 1 to 40 end with? (Justification!)
The product contains the factors 5, 10, 15, 20, 30, 35, and 40, as well as the factor 25, in which the factor 5 occurs a total of nine times.

In all other factors, the factor 5 does not occur. Since the number of trailing zeros depends on the number of factors 2 and 5, and in this case the factor 5 occurs at least nine times, the product has exactly 9 trailing zeros.