Latest TCS Aptitude Question SOLUTION: What Will Be the Remainder if 132^66^33 is divided by 5

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What Will Be the Remainder if 132^66^33 is divided by 5

Asked In TCS NILOTPAL MRINAL (9 years ago)

Unsolved Read Solution (17)

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arohibora  (9 years ago)

Just use -ve remainder theorem..
132^66^33 can be written as (130+2)^66^33
now 130 is completely divisible by 5 so its any power is also divisible....
So remainder will be from 2^66^33
This can be written as 4^33^33..
Now this can be written as(5-1)^33^33/5=(-1)^33^33/5=(-1/5),its rem=4....

Is this solution Helpfull? Yes (48) | No (5)  

Goldi kumari  (9 years ago)

unit dgit's of 132=2
66^33 it's unit digits=6
2^6=64
64 is divided by 5 then remainder=4

Is this solution Helpfull? Yes (38) | No (9)  

Ninad Raikwar  (9 years ago)

When u multiply 132*66 only find the last digit... It comes out to be *****2 and when u multiply this by 33 last digit will be 6 i.e *****6

Now we know that when there is 5 or 0 at end, no. gets completely divided by 5 so when 6 is at unit place 1 will be the remainder

Answer : 1

Is this solution Helpfull? Yes (8) | No (8)  

Faisal Noor  (9 years ago)

ANSWER: 4 or 1.

EXPLANATION: 66^33 will always have 6 in its ones place (just like 6 raised to the power of any number has 6 in its ones place). Now 132 raised to the power any number with 6 in its ones place(like 6,16,26,36,etc.) will have 4 or 6 in its one's place. Thus when divided by 5 132^66^33 will have 4 or 1 as remainder.

Is this solution Helpfull? Yes (5) | No (1)  

gautam gaurav  (9 years ago)

using -ve remainder theorm
2^66^33/5=(4)^33*33/5
=-1/5=4

Is this solution Helpfull? Yes (3) | No   

Vishnu Priya Kalyanapuram  (9 years ago)

132^66^33 this whole number can be taken as 2^6^3 for findng the remainder (taking only unit placed digits in 132,66 and 33)
units digit in 6^3 is 6
units digit in 2^6 is 2
2%5 is 2
remainder is 2

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

subhradeep de  (9 years ago)

66^33 it's unit digit=6^33=6
last digit of 132=2
2^6=64
64 is divided by 5 then remainder is=4.

Is this solution Helpfull? Yes (2) | No   

Tanvir Sarkar  (9 years ago)

answer is 1. As (even)^4k = last digit 6.(k=1,2,3,4,.....)
so 6%5=1

Is this solution Helpfull? Yes (2) | No   

Aritra Das  (9 years ago)

132^66^33/5
132=130+2
so 2^66^33
now 2^66 ends with 4
so 4^33
now 4/5 remainder is -1
so -1^33/5
final remainder -1
so remainder will be 5-1=4

Is this solution Helpfull? Yes (2) | No   

C.P.Shrikrishnan  (9 years ago)

Take the unit digit in 132
2 has only 4 cycles and if 66 is divided by 5 we get remainder as 2 so in cycles of 2 we get 4.
Next 4 has only a&6 as its cycles and when 33 is divided by 4 we get rem as 1
Therefore 4/5=4 as the numerator is smaller than the denominator.

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

bikram  (9 years ago)

132/5=2
2/5=2
2^2/5=4
2^3/5=3
2^4/5=1.
so cycle is 4.
66/4=2
132^66/5=4
4/5=1
4^2/5=1
33/4=1
4^33/5=4
ans=4.

Is this solution Helpfull? Yes (1) | No   

Deepanshu Batra  (9 years ago)

132^66^33
First Calculate last two digits of 66^33 which come out to be 96
so 132^***96/5=2^***96/5.... unit digit will come out to be 6 since 96 is divisible by 4 .... so ans has to be 6%5=1

Is this solution Helpfull? Yes (1) | No   

prema  (9 years ago)

32=130+2 i.e 130 is divisible by 5.Therefore will always leave remainder ZERO.
Now, 2^66^33 will give us required remainder.
Take 2^66 => 16^64 => On Dividing 16 by 5, Remainder=1
Therefore, 1^64^33 is equals 1.
Hence Remainder = 1

Is this solution Helpfull? Yes | No (3)  

deepika  (9 years ago)

132^66^33
first 66^33
6 power anything is 6
so 132^6
2 has 4 possibilities so 6/4=1 remainder 2
2^2 is 4 ans

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yash gupta  (9 years ago)

1
132^66 give unit digit as 4 as per power cycle
(xxx4)^33 give unit digit as 6 as per power cycle of 4
there for 1 is remainder

Is this solution Helpfull? Yes | No (4)  

Gaurav rao kadam  (9 years ago)

132^66^33--->(130+2)^66^33 Since 130 is completely divisible by 5, you only have to think about 2^66^33 again 4^33^33---> (5-1)^33^33 now 5 is completely divisible by 5 (-1)^33^33=-1 which means remainder is 5-1= 4 ans.

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Nikesh Kumar  (9 years ago)

132^66^33/5=
7^66^33/5=
(7^2)^33^33/5=(-1)^33^33/5=-1/5=4

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