Forest ServicesQ44. What is the remainder if 2^192 is divided by 6?
Detailed Solution
To find the remainder when 2^192 is divided by 6, we can observe the pattern of remainders of powers of 2 when divided by 6: 2^1 = 2 (Remainder 2) 2^2 = 4 (Remainder 4) 2^3 = 8 (Remainder 2) 2^4 = 16 (Remainder 4) The pattern of remainders is 2, 4, 2, 4... We observe that if the power of 2 is odd, the remainder is 2; if the power of 2 is even (and greater than or equal to 2), the remainder is 4.
Since the power 192 is an even number, the remainder when 2^192 is divided by 6 will be 4. This question tests number theory concepts, specifically remainders and cyclicity, which are common in CSAT.
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