Question

Determine the last digit of the number (123)^999. Any ideas how?

Answer 1

log ?

Answer 2

can u use a calculator ?

Answer 3

Oh! There's actually no log, I've just changed it to 123^999

Answer 4

Sorry

Answer 5

lol okay

Answer 6

haha , so using mod ?

Answer 7

Calculator can't solve raise to 999s. lol

Answer 8

il give a hint : last digit is the remainder u get when u divide the number by 10

Answer 9

@jricafort yeah ik ,
i thought ur qs is log ....
which can be solved using cal

Answer 10

so why dont u try to get a pattern?
like
123^1
....
123^n
does that work ?

Answer 11

@ganeshie8 Another hint perhaps?

Answer 12

second method : look for a pattern as Bswan is guiding u

Answer 13

123^1 give 3
123^2 give 9
123^3 give 7
123^4 give 1
123^5 give 3
123^6 give 9
and so on :3

Answer 14

\[123^{999} \equiv 3^{999} \equiv 3 (-1)^{449} \equiv -3 \equiv 7 \mod 10\]

Answer 15

7 is correct Bswan ^

Answer 16

u have pat each 4
take 999 mod 4=3
so take case 3
i think 7 :)

Answer 17

Nice! Got it.. @ganeshie8 & @Bswan Thank you! very helpful! :-)

Answer 18

:D
i was guessing :P

Answer 19

u could try binomial thm also for doing these kindof probs..

Answer 20

@ganeshie8 isnt that would be too much for kids ? :O

Answer 21

By binomial thm, \(123^{999} = 10K + 3^{999}\)

Answer 22

Bswan that was only to confirm ur answer, not for the OP :)

Answer 23

applying binomial thm again on 3^999 gives u : \(3^{999} = 10M + 7\)

Answer 24

you got 3 methods already... use whichever is easy for u :)

Answer 25

cool :)

Answer 26

Wow, thanks guys!

Answer 27

u wlc :)