1.

Find the number of trailing zeroes in 100!

Answer»

The number of trailing ZEROES is given by the number of powers of 10 in 100!. Each power of 10 is a combination of a power of 5 and a power of 2. Since number of powers of 5 will be more than the powers of 2, we only need to calculate the number of powers of 5 in 100!.

This can be done by GREATEST integer function.
In this solution, I will be using the BRACKET symbol for greatest integer function!!
Thus the powers of 5 in 100! are
( \frac{100}{5} ) + (\frac{100}{ {5}^{2} } ) + (\frac{100}{ {5}^{3} } )....... \\ = 20 + 4 + 0 + 0 + 0....... \\ = 24
Thus there will be 24 trailing zeroes in the end of 100!.

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