Latest CTS Aptitude Question SOLUTION: What is the remainder wen 2^35 is divided by 5?

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What is the remainder wen 2^35 is divided by 5?

Asked In CTS praveena (10 years ago)

Solved Saraswathy Read Solution (20)

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Saraswathy  (10 years ago)

We can use cyclic remainder theorem
2^1 % 5 = 2
2^2 % 5 = 4
2^3 % 5 = 3
2^4 % 5 = 1

Again
2^5 % 5 = 2
2^6 % 5 = 4
So the 1st cycle is upto the power of "4"...
So the remainder of 2^35 % 5 ll be (4k + n)th value...
35 => 4*8+3 [k=8, n=3]
If n=1, rem=2
If n=2, rem=4
If n=3, rem=3
If n=4, rem=1
Hence the remainder is 3

Ans : 3

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RAKESH  (10 years ago)

2^35 / 5
=> (2^4)^8 * 2^3 / 5
=> (5*3+1)^8 * (5+3) / 5
=> (1*3)/5
=> 3/5
=> remainder = 3

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pawan kumar chhipa  (10 years ago)

2^4 / 5 is always have reminder 1
so convert in this form like

(((2^4)^8)*(2^3))/5
((2^4)^8)/5 remainder is 1
1*(2^3)/5
8/5=3
answer is 3

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Abitha  (9 years ago)

always follow this method for finding the remainder.
eg: 2^35/5

2^1=2 2/5=2
2^2=4 4/5=4
2^3=8 8/5=3
2^4=16 16/5=1
2^5=32 32/5=2

the sequence repeats like 243124312431....

so 2 4 3 1 2 4 3 1 2 4
3 1 2 4 3 1 2 4 3 1

1st series is for 1-10 2nd series is for 11-20
then again 1st series for 21-30..

now 2^35 second series 5th element..
Its 3.

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Shikha Sinha  (9 years ago)

remainder is 3. since 2^1=2
2^2=4
2^3=8
2^4=16
2^5=32
2^6=64... so on
so the last digit with increasing power repeats as 2,4,8,6 and again the same. Dividing 35 by 4 gives 3 as remainder so the last digit have been 8,any digit ending with 8 when divided by 5 gives remainder as 3.ans

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vanmathi  (9 years ago)

2^4=unit digit is 6
2^35=[2^4]^8*2^3= 6*8=unit digit is 8
so rem is 8/5=3
reminder=3

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santhi   (10 years ago)

ans: 3
2^1=r(2)
2^2=r(4)
2^3=r(3)
2^4=r(1)
2^5=r(2).....
2^35=r(3)

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souharda  (9 years ago)

last digit of 2^35=8 so rem=3

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karthikeyank  (9 years ago)

Ans:3

(2^10*2^10*2^10)*2^5
(1024)^3*2^5
Take unit digit in 1024
4*2^5=4*32=128

128/5=remainder is 3

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sireesha reddy  (9 years ago)

2^4=16
16 mod 5=1
2^35=(2^4)^8*2^3
(1)^8*3= 3
ans =3

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shaweta  (8 years ago)

as per the rule cyclic power..

35%4=3 as remainder
which means 2^3=8 and 8%5=3 as remainder.

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darladiwakar  (9 years ago)

2^5 reminder=2
2^10 reminder=4
2^15 reminder=3
2^20 reminder=1
2^25 reminder=2
2^30 reminder=4
2^35 reminder=3
so the answer is 3

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minku  (8 years ago)

35/4=3
Now take 2^3=8
Next Divide 8 by 5
8/5=3
Therefore Remainder is 3

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Yamuna Muthusamy  (9 years ago)

The unit digit of
2^1=2
2^2=4
2^3=8
2^4=6
2^5=2
2^6=4
2^7=8
2^8=6
this unit digit value repeats for every 4 powers-power cycle
((2^4)^8)*(2^3)
take only the unit digit values,we get
(6)*8=48(refer above)
divide 48 by 5
48%5=3
Ans:3

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santhi   (9 years ago)

rem: 2^1/5=2 2^2/5=4 2^3/5=3 2^4/1 ....
35/4=rem(3)
ans:3

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vasu  (9 years ago)

power cycles and remainder cycle of 2 is:
2 1
4 2
8 3
6 0
to get the unit digit 35/4(bcoz no of power cycle is 4) the remainder is 3.power cycle 3 is equal to 8.so 8/5 remainder is 3. ans is 3

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PRADEEP KUMAR  (9 years ago)

2^1%5=2
2^2%5=4
2^3%5=3
2^4%5=1
so, 2^35=((2^4)^8)*(2^3)
=((1)^8)*(3)
=1*3
=3

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masum reza  (8 years ago)

2^35=(2^4)^8*2^3
16*8/5=1*3
=3

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VENKATESAN V G  (8 years ago)

rem 3.... cyclic of 2 is 4........ 35/4 gives 3rd cycle of 2 which is 8... dividing 8 by 5 gives 3 remainder

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Vaishnavi  (5 years ago)

divide 35 by 4 so that remainder will be 8
take the remainder 8 and divide it by 5 then we will get the answer 3

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