! digit sum..
Number Theory
Level
2
I have a positive integer 'n'>100. I take n! ,then I sum the all its digits, a number comes, then I again sum it's digit. I do it till I get a single digit . What is the single digit?
The answer is 9.
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1 solution
It's answer is 9 for all values of n greater than 6. The n! Will be multiple of 9, so it's digit sum will also be multiple of 9. If digit sum is multiple of 9, then it's digit sum will also be multiple of 9, I do it again and again, in end I will get it as 9.