If we were given a question to find the number of zero's in the product of the first 100 integers then can we use the following

we know that to find the zero's we need 5 and 2 so we can focus on the 5's

100/5 + 100/ 5^2 + 100/5^3 + 100/5^4....

we get 20 + 4 + 0 + 0 ( I know you can stop at 5^3 but just wrote the extra step for a general case)

so there will be 24 zeros? Is this approach correct and can I use it for all such questions

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