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Short answer: 1.

Long anwer: The prime factorization of 8 is 2 * 2 * 2 and the prime factorization of 11 is 11. By the Fundamental Theorem of Arithmetic, the factorization is unique and all common prime factors must appear in both lists (2, 2, 2 and 11). Since no prime divides both 8 and 11, then the only other possible answers are 1 and -1.

Because 1 > -1, the answer is 1.

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