Question 124

How many zeros would be there in $$1024!$$

Solution

The number of zeros in n! = highest power of 5 in n!

Highest power of 5 in 1024! = [$$\frac{1024}{5}$$] + [$$\frac{1024}{25}$$] +[$$\frac{1024}{125}$$] + [$$\frac{1024}{625}$$] where [ ]is the greatest integer function.

Highest power of 5 in 1024! = 204+ 40+ 8+ 1 = 253

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