Division by 240!

Number Theory Level 2

1 ! + 2 ! + 3 ! + 4 ! + … + 100 ! \large 1! +2!+3!+4!+\ldots+100!

What is the remainder when the number above is divided by 240?

33 187 73 153

Vatsal Sapra by Vatsal Sapra , 22, India

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1 solution

Vatsal Sapra
Jun 19, 2015

For n>=6 , n! is divisible by 240. Thus, when x is divided by 240, the remainder is ---

1! + 2! + 3! + 4! + 5! = 153

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