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Algebra

Cool goIITian

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10 Feb 2012 12:12:23 IST

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Write the remainder obtained when ( 1! + 2! + 3! ............ + 200! ) is divided by 14 ?

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hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

10 Feb 2012 12:46:47 IST

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for numbers greater than or equal to 14! , we have them divisible by 14.

also 7!, 8!, .... ,13! are divisible by both 2 and 7 hence divisible by 14.

so we just need to find the remainder when

1! + 2! + 3! + 4! + 5! + 6! is divided by 14.

1 + 2 + 6 + 24 + 120 + 720 = 873.

and 873-5 is divisible y 14.

answer is 5...

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