A problem from my book
Function is defined as the sum of digits of being repeated until that sum becomes a single digit. For example, [f(123456)=(1+2+3+4+5+6)=(21)=(2+1)=(3)=3.
Find the value of .
Notation
:
denotes the
factorial
notation. For example,
.
The answer is 9.
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The number 2612000 is not a special number whose sum of digits can be calculated . Actually it can be done with factorial of any number greater than 6 and answer will be same. so lets start with our solution; The number given is 2612000! so we all know that it is divisible by 9, and for divisibility by 9 the sum of digits must be a multiple of 9. so let X be the sum obtained by adding digits of 2612000!. and this X will surely be a multiple of 9 say 9a,which again means that X is divisible by 9. and if we add digits of X we will get a new number which is multiple of 9 say Y. which again means that Y is divisible by 9. and hence we will do adding the digits of sum obtained and finally come towards a one digit number which is none other than 9 as 9 is divisible by 9.hence the answer is 9.