Question

In the value of $100!$ the number of zeros at the end is

• A. 11
• B. 22
• C. 23
• D. 24

Answer 1

The correct option is D 24

zero comes at the end when 2 is multiplied with 5
so let's calculate the power of 2 in 100!
The power of 2 is the sum of $\left[\frac{100}{2}\right]=50,\left[\frac{50}{2}\right]=25,\left[\frac{25}{2}\right]=12,\left[\frac{12}{2}\right]=6,\left[\frac{6}{2}\right]=3,\left[\frac{3}{2}\right]=1,\left[\frac{1}{2}\right]=0$
where $\left[\right]$ denotes the Greatest Integer Function.
Then, power of $2=$ $50+25+12+6+3+1=97$
similarly the power of 5 is the sum of $\left[\frac{100}{5}\right]=20,\left[\frac{20}{5}\right]=4,\left[\frac{4}{5}\right]=0$
Then, the power of $5=$ $20+4=24$
but the power of 5 is less than that of 2.Hence no. of power of 5 will decide the number of 10 formed
Thus, number of 10 formed $=24$
Hence number of 0s in the end of $100!=24$