Latest self Aptitude Question SOLUTION: what will be the remainder when 720*720*720.....upto 1200 times is divided by 13.

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what will be the remainder when 720*720*720.....upto 1200 times is divided by 13.

Pulkit Mehrotra (11 years ago)

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SDeep Bhattacharya  (11 years ago)

720= (715+5)=(13*55 + 5);
So, (720)^(1200)=(13*55 + 5)^(1200);Now if we expand [(13*55 + 5)^1200],then clearly every term of the expansion except (5^1200), is divisible by 13, because except (5^1200),every other term of the expansion ocontains (13*55) as one of its factors.
So,if we can calculate the remainder when(5^1200) is divided by 13,that will be the required answer.
Now, (5^1200)=(5^2)^(600)=25^(600)=(26-1)^(600)=(13*2-1)^600;
Like same reasoning as above, every term except [(-1)^(600)] of the expansion[(13*2-1)^600] will be divisible by 13.
Therefore ,when (5^1200)is divided by 13,the remainder will be =[(-1)^(600)]=1.
So, when (720)^(1200) is divided by 13,the remainder will be = 1.
I've tried my best to explain the whole matter in very lucid style,still if u have any confusion to make out the solution,then plse dont feel hesitated to ask me for any further clarification..
Thanks to all..:-):-)

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jagannathan  (11 years ago)

720^1200/(13)
(715+5)^1200/13
715 IS DIVISIBLE BY 13. HENCE 5^1200/13 IS REMAINDER. 5^1200=>25^600=>625^300. (624+1)^300/(13). 624 IS DIVISIBLE. HENCE 1^300/13. HENCE REMAINDER =1

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