2021_IAS_Qn C15. If 3^2019 is divided by 10, then what is the remainder ?

If 3^2019 is divided by 10, then what is the remainder ?
(a)    1
(b)    3
(c)     7
(d)    9

[AbdusCSATMATH]

Remainder of (a×b×c)/10 =Remainder of (a/10)×Remainder of (b/10)×Remainder (c/10). Then,
Remainder of (3^2019)/10= Remainder of (3/10)×(Remainder of(3/10)
(We know, 3^2019=3 multiplied by 2019 times=3×3×3×...3×3×3.
=
=(3^4) multiplied by 504 times ×3^3
=81 multiplied by 504 times × 27=(81^504)×27)).
Remainder of (81^504)×27)/10=Remainder of (81/10)×Remainder of (81/10)×Remainder of (27/10)
=Remainder of

Or

Now consider negative Remainder. Then,
Remainder of (3^2019)/10 = Remainder of ((9^1008)×3)
= Remainder of (9/10)× Remainder of of (9/10)×Remainder of (3/10)= (since, (-1) multiplied by even time get 1).

[preetiduhan]

It's simplest method is unit digit of ..power of 3 repeats after at every 4 (3^1=3, 3^2=9, 3^3=27 i.e 7, 3^4=81 i.e. 1 at unit place, 3^5=1 ) ..its unit digit will repeat like 3, 7, 9, 1, 3, 7, 9, 1. so directly dividing power of 3 by 4 (2019÷4) we get 3 as remainder....so ansr will be 3^3 = 27 ÷10 = 7 as remainder

[Kishoriji]

I solved this question like this - 2019 ÷ by 4, remainder =3 then unit digit 3 to the power 3 which means 3×3×3= 27 and 7 unit digit ans . I don't know this method is correct or wrong but i thought that, this question is like unit digits question that's why i solve with this method plz respond me sir whether I'm right or wrong

[rahulpandey-ceiv]

Hey (81) whole power, how possible to divide with 10, when that is in whole power. Can you please explain this

[MoumitaSingh-md]

itnaaaa bol-bacchan ??
Bro, although ur ans is right, but u don't know the short method....iye sawas 5 sec. ka hai sirf

[guddukanwer]

Can you explain these answer series for Hindi midium plz

[danyalraza]

ye salein btayenge ki kon brashtachar h

[nmdv]

Thank you bro very much. Keep dng .