(1!+2!+3!+......100!)/100.= ...... Find the remainder ?

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HSBC244 Share
Sep 21, 2017

Answer:

Remainder is #13#

Explanation:

We know that

#1! = 1#
#2! = 2#
#3! = 6#
#4! = 24#
#5! = 120#
#6! = 720#
#7! = 5040#
#8! = 40320#
#9! = 362880#
#10! = 3,628,800#

From here on in, the numbers will always end with at least two zeroes, so we know the last two numbers won't change.

The sum of the first #10# factorials ends with a #13#, which will be the remainder.

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