Finding remainder

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What will be the remainder when 4^1000 is divided by 7? Pls explain.

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Number Systems Nkk 3 years 2 Answers 1045 views 0

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  1. Akshay Girhepuje

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    The answer is 4..
    (4^1000) =((4^3)^333)*(4^1) = (64^333)* 4

    The first term 64^333 will give remainder of 1 when divided by 7 by following the rule- (ax+1)^n/a gives remainder of 1. Since it can be written as (((7*9)+1)^333)/n

    And the second term 4 will remainder of 4 obviously.. So 1*4 =4. That’s your answer..

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    6 because power of 4 is even then last digit always 6.

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