What is the greatest common factor of 85, 4, and 17?

To determine the greatest common factor (GCF) of 85, 4, and 17, it is important to first identify the factors of each number.

The factors of 85 are 1, 5, 17, and 85. The number 85 is made up of the prime factorization (5 \times 17).

The factors of 4 are 1, 2, and 4. The prime factorization of 4 is (2^2).

The factors of 17 are 1 and 17, as it is a prime number.

The next step is to find the common factors among these three sets of factors. The only number that appears in all three sets is 1.

Since 1 is the only common factor, and it indicates that the greatest common factor of 85, 4, and 17 is indeed 1. This signifies that the numbers do not have any other larger common factors. Thus, the greatest common factor is 1 because it is universally a factor of every integer, including these three numbers.