I have been working this problem for a while and I know there must be a better way of finding the answer than I have been trying. Please help? Will you show me how to get the answer?
The question is [find the remainder when 7 to the hundredth power is divided by 9].
2007-07-12 07:58:35 · 5 answers · asked by Libby 5 in Science & Mathematics ➔ Mathematics
7^1 rem 9 = 7
7^2 rem 9 = 4
7^3 rem 9 = 1
7^4 rem 9 = 7
7^5 rem 9 = 4
7^6 rem 9 = 1
and so on.
So, 7^100 rem 9 = 7.
2007-07-12 08:09:40 · answer #1 · answered by Anonymous · 1⤊ 0⤋
There is a general pattern. 7^1 mod 9 = 7 7^2 mod 9 = 4 7^3 mod 9 = 1 7^4 mod 9 = 7 7^5 mod 9 = 4 etc etc generally 7^(3n+1) mod 9 = 7 So 7^100 mod 9 = 7
2016-05-20 22:46:28 · answer #2 · answered by Anonymous · 0⤊ 0⤋
7 = -2 (mod 9), so start by replacing 7 with (-2).
(-2)^100 = ((-2)^3)^33 * -2.
(-2)^3 = -8 = 1 (mod 9) and 1^33 = 1. Finally, 1 * -2 = -2 = 7 (mod 9).
Thus, 7^100/9 has a remainder of 7.
2007-07-12 08:06:26 · answer #3 · answered by Mathsorcerer 7 · 0⤊ 0⤋
You can never do it.
7x7x7x7x7x7x7x7x7x7.........
-----------------------------------------------
3x3
See, there is 7^10 over 9.
Nothing will ever cross out.
It will always be 7^10 over 9.
2007-07-12 08:14:39 · answer #4 · answered by Anonymous · 0⤊ 0⤋
77.7777777777...
it is a repeating number
2007-07-12 17:30:05 · answer #5 · answered by Anonymous · 0⤊ 0⤋