Answer :

To find the number of sets of factors of 264 that are co-prime with each other, identify its prime factorization and consider distinct sets of these co-prime factors. The total is 11 sets.

Finding Co-Primes Factors of 264

To solve the problem of finding the total number of sets of factors of 264 which are co-prime to each other, first consider the prime factorization of 264:

  • 264 = 2^3 × 3 × 11

Next, we identify the subsets of these prime factors that are co-prime with each other:

(2^3), (3), (11)

Thus, the different groups of co-prime sets of these factors can be:

  1. {(2^3, 3), (2^3, 11), (3, 11)}
  2. {(2^3, 3, 11)}
  3. {(2^3), (3), (11)}

Considering all distinct groups, the total number of sets of factors of 264 which are co-prime to each other is 11.

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