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# If 3^50 is divided by 4 what is the remainder ? i

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CEO
Joined: 15 Aug 2003
Posts: 3452

Kudos [?]: 928 [0], given: 781

If 3^50 is divided by 4 what is the remainder ? i [#permalink]

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01 Oct 2003, 17:06
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If 3^50 is divided by 4 what is the remainder ?

i remember there was clever shortcut to this, but cant seem to recall now..

thanks
praetorian

Kudos [?]: 928 [0], given: 781

Manager
Joined: 26 Aug 2003
Posts: 232

Kudos [?]: 13 [0], given: 0

Location: United States

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01 Oct 2003, 18:54
Well, let's see... the unit digits repeat every 4 powers. i.e 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243, ...; so if you do the following:

50 % 4 = 2

So the unit digit of 50th power should be 9, thus 9 % 4 = 1

So the answer would be 1.

Kudos [?]: 13 [0], given: 0

Senior Manager
Joined: 22 Aug 2003
Posts: 257

Kudos [?]: 13 [0], given: 0

Location: Bangalore

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02 Oct 2003, 06:43
i wud just like to add here:
If last digit is 9, i think it is not correct to claim that remainder is 1, by the argument 9%4 gives 1 as remainder. (does 19 give remainder 1 on division by 4)
i think correct method is:
3^1 = 3 % 4 gives remainder 3
3^2 = 9 % 4 gives remainder 1
3^3= 27 % 4 gives remainder 3
3^4 =81 % 4 gives remainder 1

Now, one sees a rule/law. Every even power of 3 gives remainder 1 and every odd power of 3 gives remainder 3 on division by 4.
thanks

Kudos [?]: 13 [0], given: 0

02 Oct 2003, 06:43
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