Latest TCS Aptitude Question SOLUTION: what will be the remainder when (222)^222 is divided by 7??

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(#M40024630) TCS Logical Reasoning question remainder Keep an EYE

what will be the remainder when (222)^222 is divided by 7??

Asked In TCS Akash Tiwari (10 years ago)

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padmapriya  (10 years ago)

(222^222)/7 by remainder theorem, we get remainder of 222/7 is 5.. 5^222;
5^2*111; 25^111; remind(25/7)=4; 4^111;
4^(3*37);
(4*4*4)^37;
64^37; remind(64/7)=1;
1^37=1
so the remainder is 1

Is this solution Helpfull? Yes (45) | No (3)  

ruchi  (10 years ago)

it
is 1
as 222^222>>>>5^222>>>>>>4^111=64^37>>>>>>1^37=1

Is this solution Helpfull? Yes (7) | No (4)  

Divya  (10 years ago)

i think the remainder is 4

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Kundan Kumar  (10 years ago)

Answer is 01
Using Remainder Theorem
222^222 reduces to 5^222
now,
it reduces to 4^111
again 4 * (2)^55
again 4* (1)^18 * 2
which is equal to 8/7
which gives the remainder as 01

Is this solution Helpfull? Yes (4) | No (3)  

Sruthi karuturi  (10 years ago)

the remainder is 4
222^222/7=(5^222)/7
=(25^111)/7
=(4^111)/7
=(8^55*4)/7
=(1^55*4)/7
=4/7. Hence remainder is 4

Is this solution Helpfull? Yes (2) | No (1)  

madhu  (10 years ago)

answer is 4..[because the unit digit must be divisible by 10.so,the value is 2^222...2^222 can be write like this..2^4*55+2=2^2=4(2^1=2,2^2=4,2^3=8,2^4=6,2^5=2^4*2=2..the cycle can be repeated).so,the dividend is 4..the ans is 4/7=4]

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sandy  (10 years ago)

pls someone explain the remainder theorem...

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bhuna  (10 years ago)

222^222/7->when base 222/7 it gives +5 as +ve integer and -2 as -ve integer
in order to simplify the solution i prefer -2 so(-2)^222/7
again 2^222 can be written as (-2^3)^37*2^2 (nothing but -2^222)
then (-2^3)=-8 which gives -1 as -ve integer so(+1)^37 nothing but 1 there again 2^2 was remained which gives us 4 as the answer

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kurella srikanth  (10 years ago)

from remainder theorem
222/7=remainder(5)
5^222=(25^111)
25/7=remainder4
4^111=4*4^110
4*2^55
4*1^18*2
8/7=1

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vamsi  (10 years ago)

remainder is 3

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Guru Pranav  (10 years ago)

1 is the remainder :)

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