Question

Find the number of trailing zeroes in 100!

Answer 1

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!.

If this helps, mark it as the brainliest answer. I would really appreciate it.

Answer 2

Answer:

24

Step-by-step explanation:

100/5 + 100/25= 24