set of all even numbers?

Question

Let M be the set of all even numbers from 1 to 25 and all the odd
numbers between 26 and 200.

If all the elements of M are multiplied , find the number of zeros at the end of this product.

(1)22
(2)18
(3)23
(4)21

Answer 1

Factors of 5:
10, 20, 35, 45, 55, 65, 75 (two factors), 85, 95, 105, 115, 125 (three factors), 135, 145, 155, 165, 175 (two factors), 185, 195
= 23 factors of 5
Factors of 2:
(one factor): 2, 6, 10, 14, 18, 22
(two factors): 4, 12, 20
(three factors): 8, 24
(four factors): 16
= 22 factors of 2
So we will have 22 zeros at the end of the product.