# Find the remainder using remainder theorem, when: 2^64 is divided by 3

when 2^2 is divided by 3 we have 1 as remainder

when 2^3 is divided by 3 we have 2 as remainder

when 2^4 is diviided by 3 we have 1 as remiander

when 2^5 is divided by 3 we have again 2 as remiander.

hence we can observer a pettern over here as when 2^even is diveded by 3 we get 1 remainder and when 2^odd is divided we get 2 as remainder.

in our question, we have 2^64 i.e. 2^even number hence, the remiander will be 1.

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