What are the factors of 729 in the context of its representation as x3?

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To determine the factors of 729 when expressed as x3, we first need to understand what 729 represents in terms of its prime factorization.

729 can be expressed mathematically as:

729 = 9 x 81 = 9 x 9 x 9 = 93

To break it down further:

  • 9 can be represented as 32.

So when we substitute that back into our equation:

729 = (32)3 = 36

From this prime factorization, we can conclude that 729 is equal to 36 and its factors can also be expressed as various powers of 3. The factors of 729 are therefore all numbers that can be formed by combining these prime factors in different ways, which include:

  • 1 (30)
  • 3 (31)
  • 9 (32)
  • 27 (33)
  • 81 (34)
  • 243 (35)
  • 729 (36)

Hence, all these values together represent the complete factor set of 729. To summarize, the factors of 729 when considering it as x3 are 1, 3, 9, 27, 81, 243, and 729 itself.

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