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(#M40012679) TCS question unit place Keep an EYE

what is the unit place of 2^(3^3458) ??

Asked In TCS Sudeep Kumar Yadav (12 years ago)

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Read Solution (11) :

raj  (12 years ago)

Lets take the power of 3 first...
3458%4=2 (2 is remainder that is unit place of power of 3)
so unit digit of 3^3458=3^2 =9
So whole eqaution can we written as...
2^9
Now,For 2^(9) .... 9%4=1(1 is remainder that is unit place of power of 2)
so unit digit is=2^1 = 2

Is this solution Helpfull? Yes (34) | No (6)  

Pallavi Barjatiya  (12 years ago)

we can also take the problem as 2^10374 / 8^3458
find cyclics for eithr 2 or 8
in 8's cycle we got the unit digit no. as 8,4,2,6
noe 3458/4=864 with remainder 2
so the secnd no. in cycle that is 4 will be the ans :) you can verify the ans using 2's cycle.

Is this solution Helpfull? Yes (8) | No (7)  

KOMAL AGRAHARI  (12 years ago)

2^(3^2)=2^9=2 so ans is 2

Is this solution Helpfull? Yes (5) | No (7)  

ANSHU KUMAR  (12 years ago)

answer will be 4.

Is this solution Helpfull? Yes (4) | No (5)  

Rahul singh  (12 years ago)

3's cycle is
(3)^1=3
3^2=9
3^3=27
after it the unit digits will be repeat...for ex-3^4=81(unit digit is 1 )
so we wil try to find the closest fully divisible no of 3458
the closest no(3456 which is divisible by 3 ....which means 3^3456 is unit digit is 7)
cause 3456+2=3458 so remaining two digit of power will 3^2=9.
so 2^9=512 so...
ans is 2.....

Is this solution Helpfull? Yes (2) | No (5)  

Sahil Motwani  (12 years ago)

@ pooja because the unit place cycle of 3^n repeats itself after 4 times. for instance 3^1=3
3^2=9
3^3=7(27 so at units place 7)
3^4=1(81 so at units place 1)
3^5=3 Thus the cycle is repeatng now

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MIR FIROJ ALI  (12 years ago)

3458%4=2
so unit digit of 3^3458=3^2=9
now, 2^(....9) here 9%4=1
so unit digit is=2^1=1

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Rahul singh  (12 years ago)

actually i forget one thing in my last answer......


the correct answer is

3's cycle is
(3)^1=3
3^2=9
3^3=27
3^4=81
after it the unit digits will be repeat...for ex-3^5=243(unit digit is 3 )
so we wil try to find the closest fully divisible no of 3458
the closest no(3456 which is divisible by 4 ....which means 3^3456 is unit digit is 7)
cause 3456+2=3458 so remaining two digit of power will 3^2=9.
so 2^9=512 so...
ans is 2.....

Is this solution Helpfull? Yes | No (4)  

Mayuri Sahagal  (12 years ago)

for 3^3458 at unit place u get 9.
2^9(unit place) we get 2
b'coz unit place for 2^ is 2,4,8,6 sequentially
so by that at2^9 we get 2

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pooja  (12 years ago)

MUKESH SINGH RAJPUT @ why u hv done this 3458%4=2 ...??
why u hv divided it by 4..???
plzz explain

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Haider Abbas  (12 years ago)

just look at the unit digits
2^3^8=(8)^8=64, 2 to the power 3 is 8 and 8 to the power is 64, thus on taking unit digit 4 will be the answer

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