This question was uploaded on 15/09/21 on social media accounts.
A number of zeroes are at the end of 1000 factorial (1000!). I got this question from YouTube on the channel "letsthinkcritically".
Solution:
Zero can only be obtained by multiplication of 2 and 5.
The number of 2s is definitely greater than the number of 5s.
That means the total number of zeros at the end of 1000!
= Total number of 5 in 1000!
A total number of numbers having one factor as 5:
\[= \lfloor\frac{1000}{5}\rfloor = 200\]
A total number of numbers having two factors as 5:
\[= \lfloor\frac{1000}{25}\rfloor = 40\]
A total number of numbers having three factors as 5:
\[= \lfloor\frac{1000}{125}\rfloor = 8\]
A total number of numbers having four factors as 5:
\[= \lfloor\frac{1000}{625}\rfloor = 1\]
Total number of 5s = 200 + 40 + 8 + 1 = 249
So that total number of zeroes = 249
Question based on Algebra and Equation.
