What is remainder left after dividing 1!+2!+3!+............100! by 7 ?

Answer 1

a very big number...........

Answer 2

each and everything 7! and previous is divisible by making use of 7, so we merely honestly would desire to project ourselves with one million! + 2! + 3! + 4! + 5! + 6! Dividing 7 right into one million! = one million provides 0 with a the remainder of one million. Dividing 7 into 2! = 2 provides 0 with a the remainder of two. Dividing 7 into 3! = 6 provides 0 with a the remainder of 6. Dividing 7 into 4! = 24 provides 3 with a the remainder of three. Dividing 7 into 5! = one hundred twenty provides 17 with a the remainder of one million. Dividing 7 into 6! = 720 provides 102 with a the remainder of 6. including up the remainders, i'm getting one million+2+6+3+one million+6 = 19, which if divided by making use of 7 yields 2 with a the remainder of 5. So something is 5. or you have got merely extra one million!+2!+3!+4!+5!+6! = 873, which if divided by making use of 7 you get 124 with a the remainder of 5.

Answer 3

The remainder left after dividing 1!+2!+3!+............100! by 7 is 3

Answer 4

The answer, 5, is correct. Let's shorten the work a bit.
First, all the terms from 7! on are 0(mod 7)
since they are all multiples of 7.
Next, by Wilson's theorem, 6! = -1(mod 7),
So 1! and 6! cancel each other out.
That leaves 2! + 3! + 4! + 5! to consider.
But 3! = -1(mod 7) and 5! = 120 = 1(mod 7),
so these 2 terms cancel.
That leaves 2! + 4! = 2 + 24 = 5(mod 7).

Answer 5

5

Answer 6

all the numbers from 7! remainder is 0 as they have 7 as a factor

we need to consider till 6.
1!+2!+3!+4!+5!+6!= 1 + 2 + 6+ 24+ 120+ 720
= 33+840 = 873
remainder is 873 mod 7 = 5

Answer 7

sum (mod7) = 1 + 2 + 6 + 24 + 120 + 720 (mod7)
= 1 + 2 + 6 + 3 + 1+ 6 (mod7)
= 5 (mod7)

Answer 8

Easy, I don't have the answer off the top of my head, but all you have to do is write a small simple program to do this for you. Here is how I would do this. Start off by writing a factorial function. Once you have that use it in a for-loop by adding each separate iteration of 'i' up to 100. Once you have the result of running it, divide the result by 7 and you should have the answer. Even then it will be a very big number and an integer might not be able to store it.

Answer 9

you can do all the ways in which the people who answered you said.but the easiest way is by using arithmetic progression or A.P.sum to n terms= n/2 (a+l) =50 (1+100)= 50(101)/7 =721.4
i may be wrong in my answer.but this is the best and easiest way to get the answer.if you have learn t arithmetic progressions,you will know.

Answer 10

all the num. above 6! are divisble by
the rem is the rem. of sum of n! from 1 to 6 when divided by 7. which is the rem of 873/7 = 5.

Answer 11

I'll need 5 hours.I'm not having this much time.