If x is a positive integer, then the least value of x for which x! is divisible by 100,000 is?
Can someone please explain intuitively what the question is asking? Select.
A) 5
B) 9
C) 12
D) 20
E) 30

Rationale: in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
Answer: D