! digit sum..

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

Suresh Jh
Feb 9, 2018

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.

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