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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: 3469
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If 3^50 is divided by 4 what is the remainder ? i [#permalink]  01 Oct 2003, 16:06
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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
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

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.
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
Followers: 1

Kudos [?]: 4 [0], given: 0

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

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