How mamy trailing zeroes in 1000! Using G.P. or A.P.?

Question

I figured out the way to calculate the number of trailing zeroes in 1000! Where ! Denotes factorial but I dont know how to use A.P. OR G.P. Original question:1000! is divisible by 10^n , find the largest possible integer value of n. My way to solve:I calculated the number of factors of 10 by dividing 1000/10 and got 100 then I knew that 5*2 is also 10 but factors of 2 are more than that of 5 so only calculated factors of 5 and that are hundred so total 200 factors of ten, but 25 has 2 factors of 5 so 40 more factors of 10 , and going on with powers of 5 I got value of n as 249. But indont know how to use GP or AP to solve the question , is there a way to do so if yes how?