Question 110

Find the number of zeroes at the end of 1090!

Solution

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The number of zeroes at the end of 1090! will depend on the power of 5 in the prime factorization of 1090!.
Number of powers of 5 can be calculated as 1090/5 + 218/5 + 43/5 + 8/5 = 218 + 43 + 8 + 1 = 270.
Thus, the number of zeroes at the end of 1090! are 270.

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