what is the remainder when (4!+5!+6!+...+99!) is divided by 84 ?
(1)60
(2)24
(3)30
(4)54
want to choose the answer with consuming less time.
any idea ?
2007-06-27 14:31:44 · 4 answers · asked by calculus 1 in Science & Mathematics ➔ Mathematics
7!, 8!, 9!, ..., 99! are all divisible by 84
The remainder is the same as the remainder when 4!+5!+6! divided by 84
4!+5!+6!=24+120+720=864
When divided by 84, leave the remainder 24
Answer: (2)24
2007-06-27 14:38:19 · answer #1 · answered by ? 5 · 0⤊ 0⤋
84 = 7×12 = 7×4×3, so everything from 7! up will be a multiple of 84.
So you just need 4! + 5! + 6! = 24 + 120 + 720 = 864 = 10(84) + 24, so the remainder is 24.
2007-06-27 14:38:56 · answer #2 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
I think it is 24
2007-06-27 15:04:12 · answer #3 · answered by Anonymous · 0⤊ 0⤋
uuuuuummmmmmmmmmm............idk tell me
2007-06-27 15:06:37 · answer #4 · answered by 96 2 · 0⤊ 0⤋