Factorial Power
Find the number of trailing zeroes of the above number?
Notation: is the factorial function. For example,
The answer is 0.
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1 solution
To make a zero we need a 2 and a 5. For that let's consider the last digit of each number.
( 2 0 1 ) 7 ! = ( 2 0 1 ) 5 0 4 0 , will end in 1, since the unit digit is 1.
7 2 0 1 ! will also not end either in 2 or 5 because 7 raised to any power will end only in 7,9,3 or 1. Since we will not get any 2 or 5 at the end to make a zero, therefore number of trailing zeroes = 0 .