Latest Maths Aptitude Question SOLUTION: find the remainder when 3^2014 divided by 60

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(#M40040956) MATHS Category question remainder Keep an EYE

find the remainder when
3^2014 divided by 60

Asked In Maths BHASKAR MANDAL (9 years ago)

Solved Junaid Ahmed Khan Read Solution (4)

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Junaid Ahmed Khan  (9 years ago) Best Solution

(3*3*3*3)^503 *3^2/60
21^503 *9/60
but 21^2=441 and 441/60 gives remainder 21
therefore 21^503/60 gives remainder 21
so 21*9/60=189/60
remainder will be 9
ans=9

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prudhvi  (9 years ago)

81^503 gives the remainder 21 And 2 gives a remainder of 2 only when divided by 60. Hence the remainder when 3^2014 is divided by 60 is the remainder when the product 21 × 2 is divided by 60.

Answer = 42

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BHASKAR MANDAL  (9 years ago)

@junaid ahmed khan thanks for giving the solution

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shekhar kumar  (9 years ago)

(3)^2014=(3^4)^503*3^2
using reminder rule 3^1 gives 3 (as unit place)
3^2 gives 9 (AS unit place)
3^3 gives 7 (as unit place)
3^4 gives 1 (as unit place)
hence, the repetition is followed next.
hence after solving it gives unit place 9
and when dividing it by 60 it gives 9 as reminder

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