Question

What's the reminder when 2^34 is divided by 5?
plz help

Answer 1

2^34 is a very large number, when you divide it by 5 you have no remainder.

Answer 2

I am not sure of any direct way to do this but yeah there is a logical way!
We OBVIOUSLY will not calculate the 2^34 value :P
So what we do is we find out what are the remainders at each stage and find a pattern!
Like this....
2^1 leaves remainder --- 2 --- when divided by 5
2^2 leaves remainder --- 4----when divided by 5
2^3 leaves remainder --- 3--- when divided by 5
2^4 leaves remainder --- 1----when divided by 5
2^5 leaves remainder --- 2 --- when divided by 5
2^6 leaves remainder --- 4----when divided by 5
And it goes on so we see that!
The pattern of remainder is
2,4,3,1,2,4,3,1.....
All we have to do is see which one corresponds to 34!! :)
Understood? :)

Answer 3

31

Answer 4

so 2 has order 4 mod(5)

Answer 5

@Isaiah.Feynman
Try it out with a calc! It does have a remainder! :)

Answer 6

4 i think

Answer 7

Looks like my its beyond my calculator. lol

Answer 8

XD

Answer 9

3+1

Answer 10

2^{34} conruent 2^6 congruent to 4 mod(5)

Answer 11

Exactly so it should be!
4 !! :D
Because 2^36 remainder is 1 [Because 36 is a multiple of 4]
And so 2^35 would be 3
And so 2^34 would be 4!!
Check the pattern @CoolJolie

Answer 12

how ur saying 2^36 is four@AkashdeepDeb

Answer 13

sorry 1

Answer 14

Because 2^36 has a degree of 36 and we know that 36 is a multiple of 4!
And we saw that 2^4 had a remainder of 1 too!! :)
And so did 2^8 = 256 has a remainder of 1 :D
Got it? :)
And so we trace the pattern backwards and we get 2^34 as 4 :D

Answer 15

yes ur right

Answer 16

:)

Answer 17

i thought 2^3=3 2^4=1 so 3+1=4 and

Answer 18

Haha. No!
That is a funny way though! : ' )

Answer 19

but 2^36= 3+4=7 2^7=1

Answer 20

bcoz
2^4 leaves 1 when divided by 5
hence
2^32=(2^4)^8 will leave remainder 1 when divided by 5
hence
2^34=2^2 * 2^32
so when 2^34 is divided by 5 remainder is 4