Options are:
- 20
- 21
- 22
- 23
- 24
I recently came across the above question in a competitive exam, where we get about 30 seconds to 1 minute for solving each problem. I want to if there are quick and easy methods to compute the result.
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I recently came across the above question in a competitive exam, where we get about 30 seconds to 1 minute for solving each problem. I want to if there are quick and easy methods to compute the result.
As a general rule, the number of $0$s at the end of $k!$ is equal to $$\sum_{i=1}^\infty \left\lfloor\frac{k}{5^i}\right\rfloor$$
The above expression is a measure of how many times $5$ divides $k!$.
A zero can only occur as result of multiplying 5 with 2. so consider the factors 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100 now Tolal number of 5 that can be obtained from these factor are 24.so there wiil be 24 zero.