1. Tardigrade
  2. Question
  3. Mathematics
  4. The remainder obtained when 1! + 2! + 3! + ....... + 11! is divided by 12 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The remainder obtained when $1! + 2! + 3! + ....... +\, 11!$ is divided by $12$ is

WBJEEWBJEE 2014Binomial Theorem

Solution:

Let $S=1 !+2 !+3 !+4 !+\ldots+11 !$
Here, we see that from $4 !$ to $11 !$, we always get a $12$ factor, so it is always divisible by $12$ .
Now, $1 !+2 !+3 !=1+2+6=9$
Hence, when $S$ is divided by $12$, the remainder is $9$ .