A number says it all - Conceptual thread

Here is some more fundas on numbers

factorial based questions asking no. of zeroes and max power of sum integer.

Find the no. of zeroes at the right end of 300!

for every zero, we require 10..n every 10 is made up of 5x2.
in the expression 1x2x3...300, multiples of 2 wud obviously be more than the multiples of 5...so v need to find the maximum power of 5 in 300!

300/5 = 60 (because every fifth no. is a multiple of 5)

300/25 = 12(because every mutiple of 25 has two 5s in it) or, 60/5=12

300/125 = 3 (because multiples of 125 have three 5s in it) or,
12/5 = 2

now 2 cannot be further divided by 5 so add all the quotients...60 + 12 + 2 = 74.

we might also get the same type of questions in a different form,

500! is divisible by 1000^n...what is the max. integral value of n?

now every 1000 is made up of 3 5s and 3 2s....2s are redundant...we need to count no. of 5s....so find total no. of 5s and divide by 3

500/5 = 100
100/5 = 20
20/5 = 4

100 + 20 + 4 =124

124/3 = 41.33

max integral value is 41.


500! is divisible by 99^n...what is the max. integral value of n?

now every 99 is made of two 3s and one 11. obviously 11 will be the deciding factor. so count no. of 11s for the answer

read rest of the topic in my blog.

Thanks,
Quant-Master