Latest MBA Aptitude Question SOLUTION: Find the remainder when 3^101 is divided by 77.

1) 3
2) 47
3) 48
4) 9

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(#M40014750) MBA question number systems, progressions Keep an EYE

Find the remainder when 3^101 is divided by 77.

1) 3
2) 47
3) 48
4) 9

Asked In MBA (11 years ago)

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niraj kumar  (10 years ago)

it can be solve by euler theorem..
as 3, 77 r co-prime
3^q(n)/77=1 where q(n)=77*(1-1/7)*(1-1/11)i.e 60
3^60/77=1
now remainder of(3^60*3^41)/77=remainder of (3^41)/77
&as we know remainder of 3^4/77=4
now reminder (3^41)/77=(3^40)*3
reminder of 3^(4*10)*3/77=4^10*3/77
reminder of 4^4*4^4*4^2*3/77= reminder of 256*256*48/77=reminder 25*25*48/77
is samae as reminder of 9*48/77=47
so ans reminder =47

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