Latest TCS Aptitude Question SOLUTION: 2^214^302 when divided by 9 find remainder? *mark q

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(#M40026414) TCS Numerical Ability question Keep an EYE

2^214^302 when divided by 9 find remainder? *mark q

Asked In TCS asxa asxaxax (10 years ago)

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Sachidanand Sharma  (10 years ago)

when dealing with large power try to express in terms of the divisor say here for exmaple:
2^214^302=64^208^302.
now 64= 9*7 + 1
so inner expression wud give a remainder as 1,which when raised to any power wud be 1. so the anwer is 1. if i am wrng please rectify .

Is this solution Helpfull? Yes (30) | No (18)  

arti   (10 years ago)

2^6=64 when 64/9 then remainder is 1
2^(214*302)
when 214*302 divided by 6 then ramainder will be 2
1*2^2=4
hence remaider will be 4..

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Tanu  (10 years ago)

Powers of 2 when divided by 9 gives remainder in form a series of 5 terms
2 4 8 7 5
Now 2^214 is of form 2^5n+4 so it will give remainder 7 when divided by 9.
2^214 * 2^214 * 2^214 * 2^214............upto 302 terms
7 * 7 *..................................upto 302 terms

Now when powers of 7 divided by 9 they forms a series of 3 terms 4 1 7
So 7^302 = 7^ (3n + 2)
Hence when it is divided by 9 the remainder would be 1.

Is this solution Helpfull? Yes (11) | No (3)  

sohit  (10 years ago)

7
we can write 214^302 in the form (3k+1).
Now 2^(3k+1)...where k is always odd and we can write {2^(3k)*2^1}
when we find the remainder it comes to 7

Is this solution Helpfull? Yes (9) | No (14)  

Priyanshi  (10 years ago)

7 is the answer

Is this solution Helpfull? Yes (6) | No (3)  

Shreyansh Jain  (10 years ago)

1 is the answer

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

RAHUL ROY  (10 years ago)

answer is 7

Is this solution Helpfull? Yes (2) | No   

Swapnil Dhule  (10 years ago)

7
2^1/9 gives reminder = 7
2^2/9 gives reminder = 5
2^3/9 gives reminder = 1
2^4/9 gives reminder = 7
2^5/9 gives reminder = 5
2^6/9 gives reminder = 1
hence reminder repeats periodically...
214^302/3 gives reminder=1
hence ans=7

Is this solution Helpfull? Yes (1) | No (3)  

shekhar das  (10 years ago)

Euler no of 9 is 6.
(9=3^2
Euler no 9=9*23 =6)
so divide 214^302 by 6, which will remainder 1.
therefore 2^1 gives 2, which on dividing by 9 gives 2.

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

Saloni Singh  (10 years ago)

How to solve these kind of problems,plz nyone kindly xplain in detail...

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tejal dobhal  (10 years ago)

can anyone explain in detail plz?

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jaydeep sarkar  (10 years ago)

ans: 1
214*302=64628
64628%4=0
so 2^0=1

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Soumitra Bhunia  (8 years ago)

={(2^6)^35*2^2}^302/9
={(64)^35*2^2}^302/9
=[1*4]^302/9
=[(4^3)^100*4^2]/9
=16/9
=7(Rem)

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Amit  (8 years ago)

by remainder theorem answer is 1

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Nitesh solanki  (8 years ago)

remainders are
2^1/9=2
2^2/9= 4
2^3/9= 8
2^4/9= 7
2^5/9= 5
2^6/9 = 1
2^7/9=2
cyclicity of 6 times therefore 214/6=4 is the reminder and in cyclicity fourth remainder term is 7. so 7 is the ans is this helpful

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Syed Mohd Fareed  (8 years ago)

Using the simple rule of {(a^x)/(a+1)}
when x is odd, remainder is a
when x is even, remainder is 1
So using this rule and solving we get remainder as 1

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