Remainder of $4^{96}$ divided by 6

CAT 2003 Slot 1 · QA · Easy · Number Systems

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What is the remainder when 4964^{96} is divided by 6?

  1. A.

    0

  2. B.

    2

  3. C.

    3

  4. D.

    4

Answer

D

Explanation

41 mod 6=44^1 \bmod 6 = 4, 42 mod 6=44^2 \bmod 6 = 4, 4n mod 6=44^n \bmod 6 = 4 for all positive integers nn. Thus remainder is 4.

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