How many terminating zeroes does 200! have? Choose the correct choice from the following options: A) 40 B) 48 C) 49 D) 55 E) 64
we must realize that the trailing zeros depend on the number of 10s (i.e. 10s or its multiples) in the factorial. 10=5*2, so we are looking for 5s and 2s. By virtue of being the more frequent number, we don't need to count the number of 2s, because there will always be equal or more 2s than 5s in a factorial. So, essentially we are looking for 5s and its exponents.   Start with finding 5s. 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 5s, 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= 
<gadget id="calculator">40+8+1</gadget>
<output>49</output>
49 trailing zeros.   ANSWER:49
<result>C</result>
How many terminating zeroes does 200! have?