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List all the factors of $$85. Write them all on the one line separated by a comma.

Question

List all the factors of 85. Write them all on the one line separated by a comma.

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Solution

To find the factors of 8585, we need to identify all the integers that divide 8585 without leaving a remainder.

Break Down the Problem

  1. Determine the prime factorization of 8585.
  2. List all combinations of these factors to find all divisors.

Relevant Concepts

The prime factorization of a number is the expression of that number as the product of its prime factors.

Analysis and Detail

  1. Prime Factorization:

    • 8585 can be factored into 55 and 1717, both of which are prime numbers.
    • Thus, the prime factorization of 8585 is 5×175 \times 17.
  2. Finding Factors:

    • The factors can be obtained by taking combinations of 00 to the maximum power of each prime factor:
      • 11 (the multiplicative identity),
      • 55,
      • 1717,
      • 8585 (the product of 55 and 1717).

Verify and Summarize

The full list of factors of 8585 is 1,5,17,851, 5, 17, 85. Each of these numbers divides 8585 without remainder.

Final Answer

The factors of 8585 are 1,5,17,851, 5, 17, 85.

This problem has been solved

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