How many terminating zeroes does 200! have? Choose the correct choice from the following answers
A) 40  B) 48  C) 49  D) 55  E) 64

Rationale: we must realize that the trailing zeros depend on the number of 10 s ( i . e . 10 s or its multiples ) in the factorial . 10 = 5 * 2 , so we are looking for 5 s and 2 s . by virtue of being the more frequent number , we do n ' t need to count the number of 2 s , because there will always be equal or more 2 s than 5 s in a factorial . so , essentially we are looking for 5 s and its exponents . start with finding 5 s . 200 / 5 = 40 . so we have 40 fives ( and 40 twos ) which means we ' ll have 40 zeros . if the answer was a decimal , such as 201 / 5 , round down . now look for two 5 s , that is 25 . so , 200 / 25 = 8 , so we have eight more zeros . lastly , 5 ^ 3 = 125 , and we have one such number in 200 ! , which gives us one more trailing zero . therefore , we have 40 + 8 + 1 = 49 trailing zeros . answer : c
Answer: C