If 5^r is a factor of 30!, which of the following is the maximum possible value of r?
Answers:
A) 4  B) 5  C) 6  D) 7  E) 8
5^r is a factor of 30! We need the maximum value of r   Or in other words, we need the maximum power of 5 in 30!   Powers of 5 in 30! = [30/5] + [30/25] = 7, where [x] is the integral part of x   Other way is to calculate the number of 5's in 30!   In the multiplication upto 30, we will encounter: 5, 10, 15, 20,25, 30   Each of 5, 10, 15, 20, 30 contain one power of 5   25 contains 2 powers of 5.   Hence total powers of 5 in 30!= 5 + 2= 
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
7   Correct option: 7
<result>D</result>
If 5^r is a factor of 30!, which of the following is the maximum possible value of r?