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WHAT IS THE REMAINDER WHEN 1!+2!+3!......n! is divided by 5??

WHAT IS THE REMAINDER WHEN 1!+2!+3!......n! is divided by 5??


2 Answers

jitender lakhanpal
62 Points
9 years ago

Dear Shubham,

 1! = 1

2! = 2

3! = 6

4! = 24

and all the factorials greater than 4 will be divided by 5

1!+2!+3!+4!+ (all the numbers are divided by 5 as all the factorials contain 5 )

1 +2 +6+24

33 is divided by 5 we get 3 as remainder 



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sonam kj
14 Points
9 years ago

hello shubham

since 1!+2!+3!+4! ends with 3(no is 33) and the rest no of factorials ends wth 0(as factorial of no exceding 4! have no 5and 2 whose multiplication ends with 0,ex5!=5*4*3*2*1 have 5 and 2)hence the whole ends with 3(0+3),so by divison by 5 we can logicaly see that 3 is the remainder..

hope this helps!

best of luck .

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