As simple as counting
Number Theory
Level
4
Find the number of trailing zeros of the following number:
The answer is 1300.
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1 solution
For counting number of trailing zeroes in any integer, we only need to find the number of 5's in that integer.
So, Number of 5's in 5 5 = 5
Number of 5's in 1 0 1 0 = 10
and so on except for 2 5 2 5 which contains 5 0 5's (as 25 itself contains t w o 5's)
similarly for 5 0 5 0 which contains 1 0 0 5's, 7 5 7 5 contains 1 5 0 5's and 1 0 0 1 0 0 contains 2 0 0 5's
So Total =
5 + 1 0 + 1 5 + 2 0 + 5 0 + 3 0 + 3 5 + 4 0 + 4 5 + 1 0 0 + 5 5 + 6 0 + 6 5 + 7 0 + 1 5 0 + 8 0 + 8 5 + 9 0 + 9 5 + 2 0 0 = 1 3 0 0