Question

How often does the prime factor 5 appear in product 1*2*3*4*5*...*50?

Answer 1

12 times

Explanation:

Prime factors

Those are integer numbers only divisible by 1 and themselves. Examples of prime numbers are 3,5,7,11,43

We have the product 1*2*3*4*5*...*50. The only places where the factor 5 can appear are those of the sequence 5,10,15,20,25,30,35,40,45,50

We must be careful because some of these factors have the factor 5 twice. 25=5*5 and 50=5*5*2, so the factor 5 appears once in the numbers 5,10,15,20,30,35,40,45 (8 times) and twice in the numbers 25,50 (4 times), for a total of 12 times