Latest CAT Aptitude Question SOLUTION: find the remainder when 2^40 is divided by 5

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(#M40018258) CAT question Keep an EYE

find the remainder when 2^40 is divided by 5

Asked In CAT MohanRaj (11 years ago)

Solved MP Read Solution (6)

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MP   (11 years ago)

1

2^40 = (2^4)^10= 16^10 means last digit ( unit place digit) will be 6.
so remainder will be 1 when 2^40 or 16^10 is divided by 5.

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lakshmi chaitanya  (11 years ago)

2^40=(2^4)^10=(16)^10=....6%5=1
ans:1

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P.Someshwar Reddy  (11 years ago)

Answer is 1.
2^1=2, 2^2=4, 2^3=8, 2^4=16
2^5=32, 2^6=64 2^7=128, 2^8=256
This shows for every 4 iterations the unit's digit numbers are being repeated, i.e. 2,4,8,6
2^40 is also gives a number with last digit as 6 , because(2^40)/(2^4 gives remainder zero
so when 2^40/5=(gives last digit as 6) and when it is divided by 5 gives remainder as 1

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Ravi Bhole  (11 years ago)

2^40/5 If 2^1,2^2,2^3,2^4 are divided by 5 remainders are 2,4,3,1. But remainders are repeated in the same way Means remainders are when 2^n divided by 5 are 2,4,3,1,2,4,3,1,2,4,3,1,2,4,3,1...................................
2^40/5 = (2^4)^10. Hence 2^40/5 remainder is 1 because 2^4/5 remainder is 1

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chakrapni  (11 years ago)

1 because 2^10^4=1024^4 so 4 is multiplied 4 times so we get 6 as last num when we 6 by 5 then we get 1 as remainder

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Himank Agrawal  (11 years ago)

The remainder will be equal to 1.
As squaring of 2 results in repetition of sequence 2,4,8,6 in unit place.
2^1=2 2^2=4 2^3=8 2^4=16(unit digit=6) 2^5=32(unit digit=2) and so on.
So unit digit of 2^40 is 6.
Remainder after dividing 6 by 5 is 1.

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