please give total process
2007-03-17 19:25:29 · 6 answers · asked by b. aniruddha 1 in Science & Mathematics ➔ Mathematics
n! is divisible by 7 for all n >=7 so you just have to the find the remainder when 1! + 2! + 3! + 4! + 5! + 6! = 873 is divided by 7 which is 5.
2007-03-17 19:29:27 · answer #1 · answered by Phineas Bogg 6 · 4⤊ 0⤋
every factorial from 7! onwards is divisible by 7
1! + 2! + 3! +4! + 5! + 6! = 873
On dividing 873 by 7 remainder is 5
So on dividing 873 + 7k by 7 remainder is 5
Set k = (7! + 8! + 9! + ....99! + 100! )/7 and the proof is complete
remainder on dividing 1! + 2! +....100! by 7 is 5
2007-03-18 02:32:43 · answer #2 · answered by astrokid 4 · 1⤊ 0⤋
anything > 7! divisible by 7 so consider only 1 to 6!. Taking mods you have 1 + 2 + 6 + 3 + 1 + 6 = 19 mod 7 = 5 mod 7.
2007-03-18 02:33:44 · answer #3 · answered by Tony Z 2 · 1⤊ 0⤋
well.. since 7! on up are divisible by 7, they would give 0 remainder..
So we only need to concern ourselves with
1! + 2! + 3! + 4! + 5! + 6!
1! - Remainder of 1
2! - Remainder of 2
3! - Remainder of 6
4! - Remainder of 3
5! - Remainder of 1
6! - Remainder of 6
Add these up....19
mod(19, 7) = 5
5 is your remainder
2007-03-18 02:34:35 · answer #4 · answered by Boozer 4 · 1⤊ 0⤋
1+2+3+4+....+100=(100x101)/2
from the formula sum of all consecutive nos.={n(n+1)}/2
where n=no of terms.
so,1+2+3+4+....+100=50x101=55550
1+2+3+4+....+100 divided by 7=55550/7
the quotient is 7935
and the remainder is 5..ans
2007-03-18 02:36:27 · answer #5 · answered by amrita 2 · 0⤊ 3⤋
The answer is 5. I used a function called "mod", but I'm not sure how to do it by hand.
2007-03-18 02:32:13 · answer #6 · answered by Anonymous · 0⤊ 0⤋