Trailing zeros

Instead of first finding the different powers of 5, Just constantly divide, the results obtained by 5 in the following order... 10,000/5=2,000 2,000/5=400 400/5=80 80/5=16 16/5=3 (divide to the that extent only when you get a natural number after dividing) 3/5 (we will not take into consideration this one bcz in this we will get 0.6 as an answer)

thus the total number of trailing zeros =2000+400+80+16+3=2499 this is an easy alternative for sure!!

Okay there are 10000/5 = 2000 multiples of 5 b/w 1 and 10000. The next power of 5 i.e. 25 has 10000/25 = 400 multiples b/w 1 and 10000. The next power of 5 i.e. 125 has 10000/125 = 80 multiples b/w 1 and 10000. The next power of 5 i.e. 625 has 10000/625 = 16 multiples b/w 1 and 10000. Again the next power of 5 i.e. 3125 has 10000/3125 = 3 multiples b/w 1 and 10000. Now the next power of 5 i.e. 15625 has 10000/15625 = 0.64 multiples i.e. less than 1 so we will not consider it . In the end we get 2000+400+80+16+3 = 2499 trailing zeros in 10000!